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Problems involving linear algebra arise in many contexts of scientific computation, either directly or through the replacement of continuous systems by discrete approximations. This introduction covers the practice of matrix algebra and manipulation, and the theory and practice of direct and iterative methods for solving linear simultaneous algebraic equations, inverting matrices, and determining the latent roots and vectors of matrices. Special attention is given to the important problem of error analysis and numerous examples illustrate the procedures recommended in various circumstances. The emphasis is on the reasons for selecting particular numerical methods rather than on programming or coding.
The book contains chapters on matrix algebra elimination methods of Gauss, Jordan, and Aitken, compact elimination methods of Doolittle, Crout, Banachiewicz and Cholesky, orthogonalization methods, condition, accuracy and precision, comparison of methods, measure of work, iterative and gradient methods, iterative methods for latent roots and vectors, and notes on error analysis for latent roots and vectors. Fox, Professor of Numerical Analysis at Oxford, was also Directory of their computing laboratory. Though this undergraduate text contains little directly about computers or computer languages, it has computer relevance and the author advises that teachers of ALGOL can wisely use the algorithms in the text as excercises. The Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications (IMA) is a biennial prize established in 1985 by the IMA in honour of mathematician Leslie Fox (1918-1992).
Matrix algebra.
Elimination methods of Gauss, Jordan and Aitken.
Compact elimination methods of Doolittle, Crout, Banachiewicz and Cholesky.
Orthogonalisation methods.
Condition, accuracy and precision.
Comparison of methods. Measure of work.
Iterative and gradient methods.
Iterative methods for latent roots and vectors.
Transformation methods for latent roots and vectors.
Notes on error analysis for latent roots and vectors