Multipoint Methods for Solving Nonlinear Equations

by Miodrag Petkovic, Beny Neta, Ljiljana Petkovic, Jovana Dzunic

Overview

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods.

Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology.

Product Details

ISBN-13:	9780123970138
Publisher:	Elsevier Science
Publication date:	01/03/2013
Pages:	344
Product dimensions:	6.10(w) x 9.00(h) x 0.70(d)

About the Author

Beny Neta (Naval Postgraduate School, Monterey, CA) is interested in finite elements, orbit prediction, partial differential equations, numerical solutions of ODE, shallow water equations and parallel computing.

Table of Contents

1 Basic concepts2 Two-Point methods3 Three-Point non-optimal methods4 Three-Point optimal methods5 Higher-order optimal methods6 Multipoint methods with memory7 Simultaneous methods for polynomial zeros

What People are Saying About This

From the Publisher

Provides a concise introduction to techniques and development of multipoint methods to achieve computational efficiency useful for solving many practical research problems in this new field

Editorial Reviews

"...a unified and comprehensive description of the existing root-finding methods…recommended to all those who want to find their way in the jungle of the immense number of different methods and classes of methods, which are intended to determine the roots of a scalar nonlinear equation." —Mathematical Reviews, Multipoint Methods for Solving Nonlinear Equations

"The authors are concerned with the approximate determination of simple and multiple zeros of real-valued functions of one real variable except for the last chapter which is devoted to the computation of simple and multiple (real and complex) zeros of polynomials…Quite a number of numerical examples are included to demonstrate the computational quality of the methods presented." —Zentralblatt MATH

"The authors examine and explain multipoint methods, starting with two-points and progress to three-point non-optimal and optimal methods. They then turn to higher-order optimal methods, multiple points with memory, and close with simultaneous methods for polynomial zeros." —Reference and Research Book News, October 2013

From the Publisher