This brief book on Newton’s method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. Solving Nonlinear Equations with Newton's Method contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
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Any engineer or scientist taking part in a computational project or involved in any computational science and engineering academic program will benefit from this book. Because the examples area so closely coupled to the text, this book cannot be understood without a working knowledge of MATLAB.
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8 of 8 people found the following review helpful:
4.0 out of 5 stars
Nice introduction,
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This review is from: Solving Nonlinear Equations with Newton's Method (Fundamentals of Algorithms) (Paperback)
This is a concise and practical introduction to some Newton method scheme, which can be read in a day or two if the reader has some background in numerical methods. The book sketches the main idea behind the methods and clearly explains the pros and cons of each method.I did not give 5 stars because the reader will eventually need his other book, Iterative Methods for Linear and Nonlinear Equations, SIAM 1995, in order to write one own code and get all the details right.
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Inside This Book
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First Sentence:
Nonlinear equations are solved as part of almost all simulations of physical processes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
successive residual norms, initial iterate, local convergence theory, nonlinear residual, chord method, nonlinear iteration, difference increment, iteration history, nonlinear solver, linear iterations, parabolic model, secant method, forward difference approximation, sparsity pattern, line search, termination criterion, iteration counter, error flag, sufficient decrease New!
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Nonlinear equations are solved as part of almost all simulations of physical processes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
successive residual norms, initial iterate, local convergence theory, nonlinear residual, chord method, nonlinear iteration, difference increment, iteration history, nonlinear solver, linear iterations, parabolic model, secant method, forward difference approximation, sparsity pattern, line search, termination criterion, iteration counter, error flag, sufficient decrease New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
See all 16 books this book cites
- An Introduction to Numerical Analysis by Kendall Atkinson in Back Matter
- Applied Mathematics by Charles D. Miller in Back Matter
- Iterative Methods for Solving Linear Systems (Frontiers in Applied Mathematics) by Anne Greenbaum in Back Matter
- Linear Algebra (Undergraduate Texts in Mathematics) by Larry Smith in Back Matter
- Applied Numerical Linear Algebra by James W. Demmel in Back Matter
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