Solving Nonlinear Equations with Iterative Methods

This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.

C. T. (Tim) Kelley was a Drexel Professor of Mathematics at North Carolina State University until his retirement in 2021. He is the author of five books, all published by SIAM, and more than 150 papers. He has mentored 27 Ph.D. students. He has served as editor-in-chief of SIAM Journal on Optimization and SIAM Review and has served as SIAM Vice President for Publications and Chair of the SIAM Board of Trustees. He is a member of SIAM, the American Nuclear Society, AAAS, AWM, Sigma Xi, and the Honorable Order of Kentucky Colonels. He is a Fellow of SIAM and the AAAS.