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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000000199723 | QA184 C53 1989 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Reviews 1
Choice Review
Ciarlet provides a very thorough introduction to the common numerical methods used in linear algebra and optimization theory. The text is well written; key words, phrases, and ideas are identified with italics. Keying the ideas being employed is of particular importance, as one can easily become lost in the midst of computation. There is a list of symbols with definitions provided for convenience. Several challenging exercises are included in each section; some involve computation, but most are theoretic in nature and complement the material in the text nicely for those with a good background in linear algebra and differential calculus in Banach or Hilbert spaces. The book is quite suitable for graduate students and advanced undergraduates. -J. R. Burke, Gonzaga University
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 |
