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elsevir-coverELSEVIER 2013

MULTIPOINT METHODS FOR SOLVING NONLINEAR EQUATIONS

Miodrag S. Petković, University of Niš, Serbia
Beny Neta, Naval Postgraduate School, Monterey, CA, USA
Ljiljana D. Petković, University of Niš, Serbia
Jovana Džunić, University of Niš, Serbia

ISBN: 978-0-12-397013-8

299 pages

Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations of the form f(x) = 0. Interest in multipoint methods has grown for two principal reasons. The first is that root solvers based on multipoint methods overcome theoretical limits of one point methods related to the convergence order and computational efficiency. Secondly, with the significant progress and developments made in computer hardware and software (multi-precision arithmetic and symbolic computation), implementation and convergence analysis of multipoint methods with the capability to generate root approximations of very high accuracy have become possible.
     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.
      This book offers the reader both a systematic introduction to techniques for developing multipoint methods and a unified presentation of the multipoint iterative methods constructed during the last fifty years. The results presented in the book mainly reflect the research conducted over the past decade, and are devoted to multipoint methods that attain maximal order of convergence with a fixed number of function evaluations.
      Intended as a combination of theoretical results, algorithmic aspects and symbolic computation, Multipoint Methods for Solving Nonlinear Equations serves as a text for students in math and applied math courses. It is also a reliable, well-structured professional reference for numerical analysts, engineers, physicists and computer scientists.