# Numerical Methods for Roots of Polynomials

Produk Detail:
• Author : J.M. McNamee
• Publisher : Elsevier
• Pages : 354 pages
• ISBN : 9780080489476
• Rating : /5 from reviews

## Numerical Methods for Roots of Polynomials

• Author : J.M. McNamee
• Publisher : Elsevier
• Release : 17 August 2007

Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it

## Numerical Methods for Roots of Polynomials

• Author : J.M. McNamee,Victor Pan
• Publisher : Newnes
• Release : 19 July 2013

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course

## Numerical Methods for Roots of Polynomials Part II

• Author : J.M. McNamee,V.Y. Pan
• Publisher : Elsevier Inc. Chapters
• Release : 19 July 2013

First we consider the Jenkins–Traub 3-stage algorithm. In stage 1 we defineIn the second stage the factor is replaced by for fixed , and in the third stage by where is re-computed at each iteration. Then a root. A slightly different algorithm is given for real polynomials. Another class of methods uses minimization, i.e. we try to find such that is a minimum, where . At this minimum we must have , i.e. . Several authors search along the coordinate axes or

## Numerical Methods for Engineers and Scientists

• Author : Joe D. Hoffman,Steven Frankel
• Publisher : CRC Press
• Release : 03 October 2018

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study

## Numerical Methods for Roots of Polynomials

• Author : J.M. McNamee,Victor Pan
• Publisher : Elsevier Science
• Release : 11 September 2013

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course

## Numerical Methods for Roots of Polynomials Part II

• Author : J.M. McNamee,V.Y. Pan
• Publisher : Elsevier Inc. Chapters
• Release : 19 July 2013

The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly

## Numerical Methods for Roots of Polynomials Part II

• Author : J.M. McNamee,V.Y. Pan
• Publisher : Elsevier Inc. Chapters
• Release : 19 July 2013

We discuss the secant method:where are initial guesses. In the Regula Falsi variation we start with initial guesses and such that ; after an iteration similar to the above we replace either a or b by the new value depending on which of or has the same sign as . Often one of the points gets “stuck,” and several variants such as the Illinois or Pegasus methods and variations are used to “unstick” it. We discuss convergence and efficiency of most

## Numerical Methods for Roots of Polynomials Part II

• Author : J.M. McNamee,V.Y. Pan
• Publisher : Elsevier Inc. Chapters
• Release : 19 July 2013

This chapter treats several topics, starting with Bernoulli’s method. This method iteratively solves a linear difference equation whose coefficients are the same as those of the polynomial. The ratios of successive iterates tends to the root of largest magnitude. Special versions are used for complex and/or multiple roots. The iteration may be accelerated, and Aitken’s variation finds all the roots simultaneously. The Quotient-Difference algorithm uses two sequences(with a similar one for ). Then, if the roots are

## Introduction to Numerical Analysis Using MATLAB

• Author : Butt
• Publisher : Jones & Bartlett Learning
• Release : 17 February 2009

Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for both courses in numerical analysis and as a reference for practicing engineers and scientists, this book presents the theoretical concepts of numerical analysis and the practical justification of these methods are presented through computer examples with the latest version of MATLAB. The book addresses a variety of questions ranging from the approximation of functions

## Numerical Methods for Roots of Polynomials Part II

• Author : J.M. McNamee,V.Y. Pan
• Publisher : Elsevier Inc. Chapters
• Release : 19 July 2013

We deal here with low-degree polynomials, mostly closed-form solutions. We describe early and modern solutions of the quadratic, and potential errors in these. Again we give the early history of the cubic, and details of Cardan’s solution and Vieta’s trigonometric approach. We consider the discriminant, which decides what type of roots the cubic has. Then we describe several ways (both old and new) of solving the quartic, most of which involve first solving a “resolvent” cubic. The quintic

## Fundamental Numerical Methods for Electrical Engineering

• Author : Stanislaw Rosloniec
• Publisher : Springer Science & Business Media
• Release : 17 July 2008

Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the

## Exploring Numerical Methods

• Author : Peter Linz,Richard Wang
• Publisher : Jones & Bartlett Learning
• Release : 08 December 2021