Numerical methods for roots of polynomials. Part II / J.M. McNamee and V.Y. Pan.

Format:

Book

Author/Creator:

McNamee, J. M.

Pan, V. Y., author.

Series:

Studies in computational mathematics ; 16.

Studies in computational mathematics, 1570-579X ; 16

Language:

English

Subjects (All):

Polynomials--Mathematical models.

Polynomials.

Equations, Roots of.

Physical Description:

1 online resource (xxi, 726 pages) : illustrations.

Edition:

1st edition

Place of Publication:

Waltham, Mass. : Academic Press, 2013

Waltham, MA : Academic Press, 2013.

Language Note:

English

System Details:

text file

Summary:

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. First comprehensive treatment of Root-

Contents:

Half Title; Title Page; Copyright; Dedication; Contents; Acknowledgment; Preface; Introduction; References; 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; References; 8 Graeffe's Root-Squaring Method

8.1 Introduction and History8.2 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; References; 9 Methods Involving Second or Higher Derivatives; 9.1 Introduction; 9.2 Halley's Method and Modifications; 9.2.1 History and Derivation

9.2.2 Convergence9.2.3 Composite or Multipoint Variations; 9.2.4 Multiple Roots; 9.2.5 Generalizations; 9.2.6 Simultaneous and/or Interval Methods; 9.2.7 The Super-Halley Method; 9.2.8 Acceleration Techniques; 9.3 Laguerre's Method and Modifications; 9.3.1 Derivation; 9.3.2 Convergence; 9.3.3 Multiple Roots; 9.3.4 Modifications; 9.3.5 Simultaneous Methods; 9.3.6 Bounds on Errors; 9.4 Chebyshev's Method; 9.4.1 History; 9.4.2 Derivation; 9.4.3 Convergence; 9.4.4 Variations; 9.5 Methods Involving Square Roots; 9.5.1 Introduction and History; 9.5.2 Derivation of Ostrowski's Method

9.5.3 Convergence of Ostrowski's Method9.5.4 Derivation of Cauchy's Method; 9.5.5 Convergence of Cauchy's Method; 9.5.6 Simultaneous Methods Involving Square Roots; 9.5.7 Square-Root Iterations for Multiple Roots; 9.5.8 Generalizations of the Methods Involving Square Roots; 9.5.9 Rounding Errors in Square Root Method; 9.6 Other Methods Involving Second Derivatives; 9.6.1 Miscellaneous; 9.6.2 Methods Based on Adomian's Decomposition; 9.6.3 Methods for Multiple Roots Involving Second Derivatives; 9.6.4 Simultaneous Methods Involving the Second Derivative

9.6.5 Interval Methods Involving Second Derivatives9.7 Composite Methods; 9.7.1 Methods Using First Derivatives Only; 9.7.2 An Implicit Method; 9.7.3 Composite Methods Involving the Second Derivative; 9.8 Methods Using Determinants; 9.9 Methods Using Derivatives Higher than Second; 9.9.1 Methods Using Hermite Interpolation; 9.9.2 Methods Using Inverse Interpolation; 9.9.3 Rational Interpolation; 9.9.4 Interval Methods; 9.9.5 Methods for Multiple Roots; 9.9.6 Miscellaneous Methods; 9.10 Schroeder's and Related Methods; 9.10.1 History and Definition of Schroeder's Method

9.10.2 Conditions for Convergence

Notes:

"ISSN: 1570-579X."

Includes bibliographical references and index

ISBN:

9780080931432

008093143X

OCLC:

849928254