Introduction to Numerical Analysis

✍ Scribed by Arnold Neumaier

• Publisher: Cambridge University Press
• Year: 2001
• Tongue: English
• Leaves: 365
• Edition: 1st
• Category: Library

✦ Synopsis

I teach a course in numerical methods approximately every two years and am always looking for "the ideal textbook." At this time I am using "Elementary Numerical Analysis: Third Edition" by Atkinson and Han. I examined this book to determine if it would be a better selection for the course.
This book covers all of the standard fare for the course:

) Fundamental analysis of computer error
) Solving linear systems of equations
) Interpolation and numerical differentiation
) Numerical integration
) Solving nonlinear equations
) Solving systems of nonlinear equations

The quality of the explanations is slightly weaker than in the Atkinson book, there is nothing specific to point to; I just find the Atkinson book more readable. Algorithms in both books are expressed in Matlab code, so there is no real difference there.
In conclusion, while I found that this book is certainly usable and may even be ranked as my second choice, at this time I will not be adopting in for use in my course.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1. The Numerical Evaluation of Expressions......Page 10
1.1 Arithmetic Expressions and Automatic Differentiation......Page 11
1.2 Numbers, Operations, and Elementary Functions......Page 23
1.3 Numerical Stability......Page 32
1.4 Error Propagation and Condition......Page 42
1.5 Interval Arithmetic......Page 47
1.6 Exercises......Page 62
2. Linear Systems of Equations......Page 70
2.1 Gaussian Elimination......Page 72
2.2 Variations on a Theme......Page 82
2.3 Rounding Errors, Equilibration, and Pivot Search......Page 91
2.4 Vector and Matrix Norms......Page 103
2.5 Condition Numbers and Data Perturbations......Page 108
2.6 Iterative Refinement......Page 115
2.7 Error Bounds for Solutions of Linear Systems......Page 121
2.8 Exercises......Page 128
3. Interpolation and Numerical Differentiation......Page 139
3.1 Interpolation by Polynomials......Page 140
3.2 Extrapolation and Numerical Differentiation......Page 154
3.3 Cubic Splines......Page 162
3.4 Approximation by Splines......Page 174
3.5 Radial Basis Functions......Page 179
3.6 Exercises......Page 191
4.1 The Accuracy of Quadrature Formulas......Page 188
4.2 Gaussian Quadrature Formulas......Page 196
4.3 The Trapezoidal Rule......Page 205
4.4 Adaptive Integration......Page 212
4.5 Solving Ordinary Differential Equations......Page 219
4.6 Step Size and Order Control......Page 228
4.7 Exercises......Page 234
5. Univariate Nonlinear Equations......Page 242
5.1 The Secant Method......Page 243
5.2 Bisection Methods......Page 250
5.3 Spectral Bisection Methods for Eigenvalues......Page 259
5.4 Convergence Order......Page 265
5.5 Error Analysis......Page 274
5.6 Complex Zeros......Page 282
5.7 Methods Using Derivative Information......Page 290
5.8 Exercises......Page 302
6. Systems of Nonlinear Equations......Page 310
6.1 Preliminaries......Page 311
6.2 Newton's Method and Its Variants......Page 320
6.3 Error Analysis......Page 331
6.4 Further Techniques for Nonlinear Systems......Page 338
6.5 Exercises......Page 349
References......Page 354
Index......Page 360

✦ Subjects

Математика;Вычислительная математика;