Numerical Analysis. A Second Course

✍ Scribed by James M. Ortega and Werner Rheinboldt (Auth.)

• Publisher: Elsevier Inc, Academic Press Inc
• Year: 1972
• Tongue: English
• Leaves: 201
• Series: Computer science and applied mathematics
• Category: Library

✦ Synopsis

Addresses some of the basic questions in numerical analysis: convergence theorems for iterative methods for both linear and nonlinear equations; discretization error, especially for ordinary differential equations; rounding error analysis; sensitivity of eigenvalues; and solutions of linear equations with respect to changes in the data

✦ Table of Contents

Content:
Computer Science and Applied Mathematics: A SERIES OF MONOGRAPHS AND TEXTBOOKS, Page ii
Front Matter, Page iii
Copyright, Page iv
Dedication, Page v
PREFACE, Pages xi-xii
LIST OF COMMONLY USED SYMBOLS, Page xiii
INTRODUCTION, Pages 1-4
CHAPTER 1 - LINEAR ALGEBRA, Pages 5-27
INTRODUCTION TO MATHEMATICAL STABILITY AND ILL CONDITIONING, Page 29
CHAPTER 2 - SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS, Pages 31-41
CHAPTER 3 - EIGENVALUES AND EIGENVECTORS, Pages 42-63
CHAPTER 4 - DIFFERENTIAL AND DIFFERENCE EQUATIONS, Pages 64-78
INTRODUCTION TO DISCRETIZATION ERROR, Page 79
CHAPTER 5 - DISCRETIZATION ERROR FOR INITIAL VALUE PROBLEMS, Pages 81-95
CHAPTER 6 - DISCRETIZATION ERROR FOR BOUNDARY VALUE PROBLEMS, Pages 96-114
INTRODUCTION TO CONVERGENCE OF ITERATIVE METHODS, Page 115
CHAPTER 7 - SYSTEMS OF LINEAR EQUATIONS, Pages 117-139
CHAPTER 8 - SYSTEMS OF NONLINEAR EQUATIONS, Pages 140-166
INTRODUCTION TO ROUNDING ERROR, Page 167
CHAPTER 9 - ROUNDING ERROR FOR GAUSSIAN ELIMINATION, Pages 169-193
BIBLIOGRAPHY, Page 195
INDEX, Pages 197-201