Compact Numerical Methods for Computers Linear Algebra and Function Minimisation
This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer.
New to the Second Edition
The accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software.
Formal problems in linear algebra
The singular-value decomposition and its use to solve least-squares problems
Handling larger problems
Some comments on the formation of the cross-product matrix ATA
Linear equations-a direct approach
The Choleski decomposition
The symmetric positive definite matrix again
The algebraic eigenvalue generalized problem
Real symmetric matrices
The generalized symmetric matrix eigenvalue problem
Optimization and nonlinear equations
Direct search methods
Descent to a minimum I-variable metric algorithms
Descent to a minimum II-conjugate gradients
Minimizing a nonlinear sum of squares
The conjugate gradients method applied to problems in linear algebra
Praise for the first edition
"Anyone who must solve complex problems on a small computer would be well advised to consult Nash's book for both ideas and actual procedures. Those with the luxury of a large-scale computer for their numerical work will also find much of interest here."
-Peter Castro (Eastman Kodak), Technometrics, 22 February 1980