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.

John C. Nash

A starting point
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
One-dimensional problems
Direct search methods
Descent to a minimum I-variable metric algorithms
Descent to a minimum II-conjugate gradients
Minimizing a nonlinear sum of squares
Leftovers
The conjugate gradients method applied to problems in linear algebra
Appendices
Bibliography
Index