Introduction to Numerical Linear Algebra and Optimisation

Introduction to Numerical Linear Algebra and Optimisation

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The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.show more

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'A valuable and welcome addition to the literature.' Mathematics of Computation 'Thanks to the author's sensible choice of material, clear proofs with many figures and the useful guide to the literature, the book can be wholeheartedly recommended to all those interested in this area.' Austrian Mathematical Societyshow more

Table of contents

Preface; Part I. Numerical Linear Algebra: 1. A summary of results on matrices; 2. General results in the numerical analysis of matrices; 3. Sources of problems in the numerical analysis of matrices; 4. Direct methods for the solution of linear systems; 5. Iterative methods for the solution of linear systems; 6. Methods for the calculation of eigenvalues and eigenvectors; Part II. Optimisation: 7. A review of differential calculus. Some applications; 8. General results on optimisation. Some algorithms; 9. Introduction to non-linear programming; 10. Linear programming; Bibliography and comments; Main notations used; Index.show more

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