## BookLibrarian.COM

### Read Your Favorite Books in PDF or EPUB

# Computational Theory Of Iterative Methods

Please Sign Up to Read or Download "**Computational Theory Of Iterative Methods**" eBooks in PDF, EPUB, Tuebl and Mobi. Start your **FREE** month now! Click Download or Read Now button to sign up and download/read Computational Theory Of Iterative Methods books. Fast Download Speed ~100% Satisfaction Guarantee ~Commercial & Ad Free

**📒Computational Theory Of Iterative Methods ✍ Ioannis Argyros**

**Computational Theory of Iterative Methods**

✏Author :

**Ioannis Argyros**

✏Publisher :

**Elsevier**

✏Release Date :

**2007-09-04**

✏Pages :

**504**

✏ISBN :

**0080560709**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Computational Theory of Iterative Methods Book Summary :** The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory. - Latest convergence results for the iterative methods - Iterative methods with the least computational cost - Iterative methods with the weakest convergence conditions - Open problems on iterative methods

**📒Aspects Of The Computational Theory For Certain Iterative Methods ✍ Ioannis Konstantinos Argyros**

**Aspects of the Computational Theory for Certain Iterative Methods**

✏Author :

**Ioannis Konstantinos Argyros**

✏Publisher :

**Polimetrica s.a.s.**

✏Release Date :

**2009**

✏Pages :

**571**

✏ISBN :

**9788876991516**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Aspects of the Computational Theory for Certain Iterative Methods Book Summary :**

**📒A Contemporary Study Of Iterative Methods ✍ A. Alberto Magrenan**

**A Contemporary Study of Iterative Methods**

✏Author :

**A. Alberto Magrenan**

✏Publisher :

**Academic Press**

✏Release Date :

**2018-02-13**

✏Pages :

**400**

✏ISBN :

**9780128094938**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏A Contemporary Study of Iterative Methods Book Summary :** A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

**Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self Adjoint Boundary Value Problems**

✏Author :

**ENGELI**

✏Publisher :

**Birkhäuser**

✏Release Date :

**2012-12-06**

✏Pages :

**107**

✏ISBN :

**9783034872249**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self Adjoint Boundary Value Problems Book Summary :**

**📒Iterative Methods And Their Dynamics With Applications ✍ Ioannis Konstantinos Argyros**

**Iterative Methods and Their Dynamics with Applications**

✏Author :

**Ioannis Konstantinos Argyros**

✏Publisher :

**CRC Press**

✏Release Date :

**2017-07-12**

✏Pages :

**365**

✏ISBN :

**9781351649506**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Methods and Their Dynamics with Applications Book Summary :** Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.

**📒Intelligent Numerical Methods Ii Applications To Multivariate Fractional Calculus ✍ George A. Anastassiou**

**Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus**

✏Author :

**George A. Anastassiou**

✏Publisher :

**Springer**

✏Release Date :

**2016-04-27**

✏Pages :

**116**

✏ISBN :

**9783319336060**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus Book Summary :** In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.

**📒Computational Methods For Linear Integral Equations ✍ Prem Kythe**

**Computational Methods for Linear Integral Equations**

✏Author :

**Prem Kythe**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2002-04-26**

✏Pages :

**508**

✏ISBN :

**0817641920**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Computational Methods for Linear Integral Equations Book Summary :** This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

**📒Iterative Algorithms 2 ✍ Ioannis K. Argyros**

**Iterative Algorithms 2**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**Nova Science Publishers**

✏Release Date :

**2016-09-01**

✏Pages :

**360**

✏ISBN :

**1634858794**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Algorithms 2 Book Summary :** The study of iterative methods began several years ago in order to find the solutions of problems where mathematicians cannot find a solution in closed form. In this way, different studies related to different methods with different behaviors have been presented over the last decades. Convergence conditions have become one of the most studied topics in recent mathematical research. One of the most well-known conditions are the Kantorovich conditions, which has allowed many researchers to experiment with all kinds of conditions. In recent years, several authors have studied different modifications of the mentioned conditions considering inter alia, H�lder conditions, alpha-conditions or even convergence in other spaces. In this monograph, the authors present the complete work within the past decade on convergence and dynamics of iterative methods. It acts as an extension of their related publications in these areas. The chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to allow the reader to refer to previous ideas. For these reasons, several advanced courses can be taught using this book. This book intends to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable for researchers, graduate students and seminars in the above subjects, and it would be an excellent addition to all science and engineering libraries.

**📒Iterative Methods For Linear Systems ✍ Maxim A. Olshanskii**

**Iterative Methods for Linear Systems**

✏Author :

**Maxim A. Olshanskii**

✏Publisher :

**SIAM**

✏Release Date :

**2014-07-21**

✏Pages :

**244**

✏ISBN :

**9781611973464**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Methods for Linear Systems Book Summary :** Iterative Methods for Linear Systems÷offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.÷÷

**📒Numerical Methods In Computational Electrodynamics ✍ Ursula van Rienen**

**Numerical Methods in Computational Electrodynamics**

✏Author :

**Ursula van Rienen**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2012-12-06**

✏Pages :

**375**

✏ISBN :

**9783642568022**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Methods in Computational Electrodynamics Book Summary :** treated in more detail. They are just specimen of larger classes of schemes. Es sentially, we have to distinguish between semi-analytical methods, discretiza tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).

**📒Iterative Methods For Toeplitz Systems ✍ Michael K. Ng**

**Iterative Methods for Toeplitz Systems**

✏Author :

**Michael K. Ng**

✏Publisher :

**Numerical Mathematics and Scie**

✏Release Date :

**2004**

✏Pages :

**350**

✏ISBN :

**0198504209**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Methods for Toeplitz Systems Book Summary :** Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyze new methods for other types of problems and applications.

**📒The Theory And Applications Of Iteration Methods ✍ Ioannis K. Argyros**

**The Theory and Applications of Iteration Methods**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**CRC Press**

✏Release Date :

**2018-05-04**

✏Pages :

**368**

✏ISBN :

**9781351408974**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏The Theory and Applications of Iteration Methods Book Summary :** The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.

**📒Numerical Analysis ✍ L. Ridgway Scott**

**Numerical Analysis**

✏Author :

**L. Ridgway Scott**

✏Publisher :

**Princeton University Press**

✏Release Date :

**2011-04-18**

✏Pages :

**344**

✏ISBN :

**1400838967**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Analysis Book Summary :** Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

**📒Numerical Methods In Finance ✍ Paolo Brandimarte**

**Numerical Methods in Finance**

✏Author :

**Paolo Brandimarte**

✏Publisher :

**John Wiley & Sons**

✏Release Date :

**2003-10-13**

✏Pages :

**432**

✏ISBN :

**9780471461692**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Methods in Finance Book Summary :** Balanced coverage of the methodology and theory of numericalmethods in finance Numerical Methods in Finance bridges the gap between financialtheory and computational practice while helping students andpractitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numericalanalysis and provides background material that suits the needs ofstudents from both financial engineering and economicsperspectives. Classical numerical analysis methods; optimization,including less familiar topics such as stochastic and integerprogramming; simulation, including low discrepancy sequences; andpartial differential equations are covered in detail. Extensiveillustrative examples of the application of all of thesemethodologies are also provided. The text is primarily focused on MATLAB-based application, but alsoincludes descriptions of other readily available toolboxes that arerelevant to finance. Helpful appendices on the basics of MATLAB andprobability theory round out this balanced coverage. Accessible forstudents-yet still a useful reference for practitioners-NumericalMethods in Finance offers an expert introduction to powerful toolsin finance.

**📒Iterative Methods For Large Linear Systems ✍ David R. Kincaid**

**Iterative Methods for Large Linear Systems**

✏Author :

**David R. Kincaid**

✏Publisher :

**Academic Press**

✏Release Date :

**2014-05-10**

✏Pages :

**350**

✏ISBN :

**9781483260204**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Methods for Large Linear Systems Book Summary :** Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.

**📒Classical And Modern Numerical Analysis ✍ Azmy S. Ackleh**

**Classical and Modern Numerical Analysis**

✏Author :

**Azmy S. Ackleh**

✏Publisher :

**CRC Press**

✏Release Date :

**2009-07-20**

✏Pages :

**628**

✏ISBN :

**1420091581**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Classical and Modern Numerical Analysis Book Summary :** Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

**📒Newton Methods ✍ Ioannis K. Argyros**

**Newton Methods**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**Nova Publishers**

✏Release Date :

**2005**

✏Pages :

**404**

✏ISBN :

**1594540527**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Newton Methods Book Summary :** This self-contained treatment offers a contemporary and systematic development of the theory and application of Newton methods, which are undoubtedly the most effective tools for solving equations appearing in computational sciences. Its focal point resides in an exhaustive analysis of the convergence properties of several Newton variants used in connection to specific real life problems originated from astrophysics, engineering, mathematical economics and other applied areas. What distinguishes this book from others is the fact that the weak convergence conditions inaugurated here allow for a wider applicability of Newton methods; finer error bounds on the distances involved, and a more precise information on the location of the solution. These factors make this book ideal for researchers, practitioners and students.

**📒Theory Of Difference Equations Numerical Methods And Applications By V Lakshmikantham And D Trigiante ✍ Lakshmikantham**

**Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante**

✏Author :

**Lakshmikantham**

✏Publisher :

**Elsevier**

✏Release Date :

**1988-05-01**

✏Pages :

**322**

✏ISBN :

**0080958699**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante Book Summary :** In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

**📒Computational Modelling Of Concrete Structures ✍ Nenad Bicanic**

**Computational Modelling of Concrete Structures**

✏Author :

**Nenad Bicanic**

✏Publisher :

**CRC Press**

✏Release Date :

**2010-02-24**

✏Pages :

**836**

✏ISBN :

**9781439859575**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Computational Modelling of Concrete Structures Book Summary :** Since 1984 the EURO-C conference series (Split 1984, Zell am See 1990, Innsbruck 1994, Badgastein 1998, St Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010) has provided a forum for academic discussion of the latest theoretical, algorithmic and modelling developments associated with computational simulations of concrete and concrete structure

**📒Convergence And Applications Of Newton Type Iterations ✍ Ioannis K. Argyros**

**Convergence and Applications of Newton type Iterations**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2008-06-12**

✏Pages :

**56**

✏ISBN :

**9780387727431**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Convergence and Applications of Newton type Iterations Book Summary :** This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.

**Iterative Methods in Scientific Computing and Their Applications**

✏Author :

**Raymond Chan**

✏Publisher :

**Springer**

✏Release Date :

**1997-04**

✏Pages :

**384**

✏ISBN :

**UVA:X004190824**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Iterative Methods in Scientific Computing and Their Applications Book Summary :** Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such a gap in the literature.

**📒Tensor Numerical Methods In Scientific Computing ✍ Boris N. Khoromskij**

**Tensor Numerical Methods in Scientific Computing**

✏Author :

**Boris N. Khoromskij**

✏Publisher :

**Walter de Gruyter GmbH & Co KG**

✏Release Date :

**2018-06-11**

✏Pages :

**379**

✏ISBN :

**9783110365917**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Tensor Numerical Methods in Scientific Computing Book Summary :** The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

**📒Functions Of Matrices ✍ Nicholas J. Higham**

**Functions of Matrices**

✏Author :

**Nicholas J. Higham**

✏Publisher :

**SIAM**

✏Release Date :

**2008**

✏Pages :

**425**

✏ISBN :

**9780898717778**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Functions of Matrices Book Summary :** A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

**📒The Theory Of Matrices In Numerical Analysis ✍ Alston S. Householder**

**The Theory of Matrices in Numerical Analysis**

✏Author :

**Alston S. Householder**

✏Publisher :

**Courier Corporation**

✏Release Date :

**2013-06-18**

✏Pages :

**272**

✏ISBN :

**9780486145631**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏The Theory of Matrices in Numerical Analysis Book Summary :** This text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations and finding characteristic roots. Topics include norms, bounds and convergence; localization theorems; more. 1964 edition.

**📒Numerical Mathematics ✍ Alfio Quarteroni**

**Numerical Mathematics**

✏Author :

**Alfio Quarteroni**

✏Publisher :

**Springer Science & Business Media**

✏Release Date :

**2010-11-30**

✏Pages :

**657**

✏ISBN :

**9783540498094**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Mathematics Book Summary :** This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

**📒Elements Of Statistical Computing ✍ R.A. Thisted**

**Elements of Statistical Computing**

✏Author :

**R.A. Thisted**

✏Publisher :

**Routledge**

✏Release Date :

**2017-10-19**

✏Pages :

**448**

✏ISBN :

**9781351452755**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Elements of Statistical Computing Book Summary :** Statistics and computing share many close relationships. Computing now permeates every aspect of statistics, from pure description to the development of statistical theory. At the same time, the computational methods used in statistical work span much of computer science. Elements of Statistical Computing covers the broad usage of computing in statistics. It provides a comprehensive account of the most important computational statistics. Included are discussions of numerical analysis, numerical integration, and smoothing. The author give special attention to floating point standards and numerical analysis; iterative methods for both linear and nonlinear equation, such as Gauss-Seidel method and successive over-relaxation; and computational methods for missing data, such as the EM algorithm. Also covered are new areas of interest, such as the Kalman filter, projection-pursuit methods, density estimation, and other computer-intensive techniques.

**📒Numerical Methods Of Statistics ✍ John F. Monahan**

**Numerical Methods of Statistics**

✏Author :

**John F. Monahan**

✏Publisher :

**Cambridge University Press**

✏Release Date :

**2001-02-05**

✏Pages :

**428**

✏ISBN :

**0521791685**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Methods of Statistics Book Summary :** This 2001 book provides a basic background in numerical analysis and its applications in statistics.

**📒A Survey Of Preconditioned Iterative Methods ✍ Are Magnus Bruaset**

**A Survey of Preconditioned Iterative Methods**

✏Author :

**Are Magnus Bruaset**

✏Publisher :

**CRC Press**

✏Release Date :

**1995-05-05**

✏Pages :

**176**

✏ISBN :

**0582276543**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏A Survey of Preconditioned Iterative Methods Book Summary :** The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are well suited for the kind of systems arising from the discretization of partial differential equations. The focus of this presentation is on the family of Krylov subspace solvers, of which the Conjugate Gradient algorithm is a typical example. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. When solving linear systems by iteration, a preconditioner is usually introduced in order to speed up convergence. In many cases, the selection of a proper preconditioner is crucial to the resulting computational performance. For this reason, this book pays special attention to different preconditioning strategies. Although aimed at a wide audience, the presentation assumes that the reader has basic knowledge of linear algebra, and to some extent, of partial differential equations. The comprehensive bibliography in this survey is provides an entry point to the enormous amount of published research in the field of iterative methods.

**📒Numerical Analysis For Scientists And Engineers ✍ Madhumangal Pal**

**Numerical Analysis for Scientists and Engineers**

✏Author :

**Madhumangal Pal**

✏Publisher :

**Alpha Science International Limited**

✏Release Date :

**2007**

✏Pages :

**654**

✏ISBN :

**UCSC:32106019051066**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Numerical Analysis for Scientists and Engineers Book Summary :** Numerical Analysis for Scientists and Engineers develops the subject gradually by illustrating several examples for both the beginners and the advanced readers using very simple language. The classical and recently developed numerical methods are derived from mathematical and computational points of view. Different aspects of errors in computation are discussed in detailed. Some finite difference operators and different techniques to solve difference equations are presented here. Various types of interpolation, including cubic-spline, methods and their applications are introduced. Direct and iterative methods for solving algebraic and transcendental equations, linear system of equations, evaluation of determinant and matrix inversion, computation of eigenvalues and eigenvectors of a matrix are well discussed in this book. Detailed concept of curve fitting and function approximation, differentiation and integration (including Monte Carlo method) are given. Many numerical methods to solve ordinary and partial differential equations with their stability and analysis are also presented. The algorithms and programs in C are designed for most of the numerical methods.

**📒Computational Methods In Nonlinear Analysis ✍ Ioannis K. Argyros**

**Computational Methods in Nonlinear Analysis**

✏Author :

**Ioannis K. Argyros**

✏Publisher :

**World Scientific**

✏Release Date :

**2013**

✏Pages :

**592**

✏ISBN :

**9789814405836**

✏Available Language :

**English, Spanish, And French**

**Click Here To Get Book**

**✏Computational Methods in Nonlinear Analysis Book Summary :** The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.