Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles

Solving Transcendental Equations is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations. Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is when this book is most useful.

Solving Transcendental Equations is unique in that it:

• Is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval. The book also describes the spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding.
• Includes three chapters on analytical methods—explicit solutions, regular perturbation expansions, and singular perturbation series (including hyperasymptotics)—unlike other books that provide only numerical algorithms for solving algebraic and transcendental equations.

MATLAB is used to solve numerous examples throughout the book.