Numerical Methods for Roots of Polynomials - Part II, Volume 16

1st Edition

Authors: J.M. McNamee Victor Pan
Hardcover ISBN: 9780444527301
eBook ISBN: 9780080931432
Imprint: Elsevier Science
Published Date: 22nd July 2013
Page Count: 728
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Table of Contents






Chapter 7. Bisection and Interpolation Methods

7.1 Introduction and History

7.2 Secant Method and Variations

7.3 The Bisection Method

7.4 Methods Involving Quadratics

7.5 Methods of Higher Order or Degree

7.6 Rational Approximations

7.7 Hybrid Methods

7.8 Parallel Methods

7.9 Multiple Roots

7.10 Method of Successive Approximation

7.11 Miscellaneous Methods Without Using Derivatives

7.12 Methods Using Interval Arithmetic

7.13 Programs


Chapter 8. Graeffe’s Root-Squaring Method

8.1 Introduction and History

8.2 The Basic Graeffe Process

8.3 Complex Roots

8.4 Multiple Modulus Roots

8.5 The Brodetsky–Smeal–Lehmer Method

8.6 Methods for Preventing Overflow

8.7 The Resultant Procedure and Related Methods

8.8 Chebyshev-Like Processes

8.9 Parallel Methods

8.10 Errors in Root Estimates by Graeffe Iteration

8.11 Turan’s Methods

8.12 Algorithm of Sebastião e Silva and Generalizations

8.13 Miscellaneous

8.14 Programs


Chapter 9. Methods Involving Second or Higher Derivatives

9.1 Introduction

9.2 Halley’s Method and Modifications

9.3 Laguerre’s Method and Modifications

9.4 Chebyshev’s Method

9.5 Methods Involving Square Roots

9.6 Other Methods Involving Second Derivatives


Chapter 10. Bernoulli, Quotient-Difference, and Integral Methods

10.1 Bernoulli’s Method for One Dominant Root

10.2 Bernoulli’s Method for Complex and/or Multiple Roots

10.3 Improvements and Generalizations of Bernoulli’s Method

10.4 The Quotient-Difference Algorithm

10.5 T


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 on that topic.

Key Features

  • First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded
  • Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate
  • Proves invaluable for research or graduate course


Primary Markets: Academic faculty and libraries

Secondary Market: Industry (engineering)


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© Elsevier Science 2013
Elsevier Science
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"...a well-written handbook of numerical methods for polynomial root-solving...covers most of the traditional methods for well as a great many invented in the last few decades of the 20th and early 21st centuries."--MathSciNet, Numerical Methods for Roots of Polynomials - Part II

"This book comprehensively covers traditional and latest methods on the calculation of roots of polynomials. The readers will benefit from this book greatly since these numerical methods in this book are accurate practical and have wide applications in control theory, information processing, statistics, etc. This book is well-written and accessible…"--Zentralblatt MATH, 1279.65053
"In this second of two parts, McNamee and Pan describe methods that are mostly numerical, or iterative, though they do devote one chapter to analytic methods for polynomials of degree up to five. Readers only need knowledge of polynomials at the senior high-school level, they say, but should have completed at least undergraduate courses in calculus and linear algebra."--
Reference & Research Book News, October 2013

About the Authors

J.M. McNamee Author

Affiliations and Expertise

York University, Toronto, Canada

Victor Pan Author