An Introduction to Numerical Linear Algebra With Exercises

• ISBN13: 9780195003253
• ISBN10: 019500325X
• Format: Hardcover
• Copyright: 1965-12-31
• Publisher: Oxford University Press

Summary

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.

Table of Contents

Introduction

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 Root and Vectors

Notes on Error Analysis for Latent Roots and Vectors

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