Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles (Other Titles in Applied Mathematics) by John P. Boyd (PDF)

Description

Transcendental equations arise in every branch of science and engineering. While some of these equations are easy to solve, many are not. When confronted with such an equation, this book serves as an indispensable resource. The author’s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. This book is the first to describe the Chebyshev-proxy rootfinder, the most reliable way to find all zeros of a smooth function on an interval, and the spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding. Unlike other books on numerical rootfinding, it includes three chapters on analytical methods – explicit solutions, regular perturbation expansions, and singular perturbation series (including hyperasymptotics). While this book is written for specialists in numerical analysis, it can be used for introductory and advanced numerical analysis classes, and as a reference for anyone working with difficult equations.

User’s Reviews

Editorial Reviews: Book Description A guide to numerical methods for finding roots of single or coupled algebraic equations. Book Description Many transcendental equations are hard to solve. This book, aimed at numerical analysts, is an indispensable resource for finding roots of algebraic equations. In addition to presenting analytic methods in detail, it is the first book to describe the Chebyshev-proxy rootfinder and the spectrally enhanced Weyl bisection/marching triangles method. About the Author John P. Boyd joined the faculty at the University of Michigan in 1977 and has been Professor of Atmospheric, Oceanic, and Space Science in the College of Engineering since 1988. Concurrently, he was the founding associate director of the Laboratory for Scientific Computation (now the Michigan Institute for Computational Discovery and Engineering). He has published 240 journal articles in atmospheric and oceanic dynamics, nonlinear waves, physics, and Chebyshev, Fourier and RBF spectral methods. Read more

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