This republication 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.
Author(s): James M. Ortega
Series: Classics in applied mathematics 3
Publisher: Society for Industrial and Applied Mathematics
Year: 1987
Language: English
Pages: 217
City: Philadelphia
Numerical Analysis A Second Course......Page 1
Contents......Page 10
Preface......Page 14
List of Commonly Used Symbols......Page 16
INTRODUCTION......Page 18
CHAPTER I LINEAR ALGEBRA......Page 22
PART I MATHEMATICAL STABILITY AND ILL CONDITIONING......Page 46
CHAPTER 2 SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS......Page 48
CHAPTER 3 EIGENVALUES AND EIGENVECTORS......Page 59
CHAPTER 4 DIFFERENTIAL AND DIFFERENCE EQUATIONS......Page 81
PART II DISCRETIZATION ERROR......Page 96
CHAPTER 5 DISCRETIZATION ERROR FOR INITIAL VALUE PROBLEMS......Page 98
CHAPTER 6 DISCRETIZATION ERROR FOR BOUNDARY VALUE PROBLEMS......Page 113
PART III CONVERGENCE OF ITERATIVE METHODS......Page 132
CHAPTER 7 SYSTEMS OF LINEAR EQUATIONS......Page 134
CHAPTER 8 SYSTEMS OF NONLINEAR EQUATIONS......Page 157
PART IV ROUNDING ERROR......Page 184
CHAPTER 9 ROUNDING ERROR FOR GAUSSIAN ELIMINATION......Page 186
BIBLIOGRAPHY......Page 212
INDEX......Page 214
