Product Description
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference.
For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Average Customer Review:
0 of 0 people found the following review helpful:
Excellent, 2008-10-24
I have to linearise a mathematical model for a Computational Fluid Dynamics problem. I have many books on CFD which all mention Newtons Method for linearisation, however I have struggled with their description of Newtons Method. Fortunately the book by Dennis and Schnabel is first class and I would highly recomend this book for anyone working on CFD problems. Newtons Method now seems straight forward, thanks to this book.
2 of 2 people found the following review helpful:
SIAM calls this book a "Classic" for good reason. , 2006-09-25
The ultimate self-teaching book for Newton-type algorithms that address small or large systems of nonlinear equations. A comprehensive treatment of general unconstrained optimization, least-squares optimization, and also well-determined systems. Unusually well-written, with a nice blend between underlying theory and practical implementation requirements. Complete pseudo-code within the appendix enables one to create their own program in any language. Alternatively, Fortran source code created by the authors (UNCMIN) can be obtained from Netlib on the web. SIAM calls this book a "Classic" for good reason.
23 of 23 people found the following review helpful:
I understood it!, 2000-12-01
Looking for a text that explains the maths and the implementation of optimisation? I needed to write a program that included numerical optimisation, but I didn't understand the maths. I'd tried to read some other books on the subject, but I gave up because they presumed too much background knowledge and because they were written in an academic format (all proofs, greek letters and algebra) too obscure for me to wade through.This book explains everything in plain english. When there is a new concept to be introduced, they begin with a practical example of the problem and then step through the solution. Any proofs are accompanied by graphs and words. The emphasis is on practicality and concepts rather than algebraic rigour.
I recommend this book to anyone who needs to create their own optimisations, or who wants to understand what goes on inside their software.