Kelley C.T. Solving nonlinear equations with Newton's method

Philadelphia, Society for Industrial and Applied Mathematics (SIAM), 2003. — 119 p. — (Fundamentals of Algorithms).This small book on Newton's method is a user-oriented guide to algorithms and implementation. Its purpose is to show, via algorithms in pseudocode, in MatLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem and write an efficient solver or apply one written by others. The computational examples in this book were done with MatLAB v6.5 on an Apple Macintosh G4 and a SONY VAIO. The MatLAB codes for the solvers and all the examples accompany this book. MatLAB is an excellent environment
for prototyping and testing and for moderate-sized production work. I have used the three main solvers nsold.m, nsoli.m, and brsola.m from the collection of MatLAB codes in my own research. The codes were designed for production work on small- to medium-scale problems having at most a few thousand unknowns. Large-scale problems are best done in a compiled language with a high-quality public domain code.