Although the computing facilities available to scientists are becoming more powerful, the problems they are addressing are increasingly complex. The mathematical methods for simplifying the computing procedures are therefore as important as ever. Microcomputer Algorithms: Action from Algebra stresses the mathematical basis behind the use of many algorithms of computational mathematics, providing detailed descriptions on how to generate algorithms for a large number of different uses.
Covering a wide range of mathematical and physical applications, the book contains the theory of 25 algorithms. The mathematical theory for each algorithm is described in detail prior to discussing the algorithm in full, with complete program listings. The book presents the algorithms in modular form, allowing for easy interpretation, for the adaptation to readers' specific requirements without difficulty, and for use with various microcomputers.
Blending mathematics and programming in one volume, this book will be of broad interest to all scientists and engineers, particularly those physicists using microcomputers for scientific problem handling. Students handling numerical data for research projects will also find the book useful.
Table of Contents
Root-finding methods and their application
The Richardson extrapolation method
Some interpolation and extrapolation methods
The matrix inverse and generalized inverse
The matrix eigenvalue problem
Two perturbation methods
Finite difference eigenvalue calculations
Recurrence relation methods
Two research problems
"… a practical and valuable resource for researchers and teachers in scientific or mathematical computing who wish to use, or to explain to others, the specific and useful microprogramming style … for using small capacity computer systems more efficiently. A number of new and unorthodox methods are introduced and some algorithms have characteristics which have yet to be fully explored. This aspect will add spice to the appeal of the book to researchers in numerical methods generally."
-The Australian Computer Journal