Introduction to Numerical Linear Algebra and Optimisation

Introduction to Numerical Linear Algebra and Optimisation

by Philippe G. Ciarlet
     
 

ISBN-10: 0521339847

ISBN-13: 9780521339841

Pub. Date: 08/25/1989

Publisher: Cambridge University Press

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is

Overview

Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is divided into two parts. The first part deals with numerical linear algebra (numerical analysis of matrices, direct and indirect methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimizations (general algorithms, linear and nonlinear programming). Summaries of basic mathematics are provided, proof of theorems are complete yet kept as simple as possible, applications from physics and mechanics are discussed, a great many exercises are included, and there is a useful guide to further reading.

Product Details

ISBN-13:
9780521339841
Publisher:
Cambridge University Press
Publication date:
08/25/1989
Series:
Cambridge Texts in Applied Mathematics Series, #4
Edition description:
New Edition
Pages:
452
Product dimensions:
5.98(w) x 8.98(h) x 1.02(d)

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.

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