A first course in numerical analysis
Book Description
Outstanding text treats numerical analysis with mathematical rigor, but relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency. Problems―some strictly mathematical, others requiring a computer―appear at the end of each chapter.
Table Of Content
Preface to the Dover Edition; Preface to the Second Edition; Notation
Chapter 1. Introduction and Preliminaries
1.1 What Is Numerical Analysis?
1.2 Sources of Error
1.3 Error Definitions and Related Matters
1.3-1 Significant digits; 1.3-2 Error in functional Evaluation; 1.3-3 Norms
1.4 Roundoff Error
1.4-1 The Probabilistic Approach to Roundoff: A Particular Example
1.5 Computer Arithmetic
1.5-1 Fixed-Point Arithmetic; 1.5-2 Floating-Point Numbers; 1.5-3 Floating-Point Arithmetic; 1.5-4 Overflow and Underflow; 1.5-5 Single- and Double-Precision Arithmetic
1.6 Error Analysis
1.6-1 Backward Error Analysis
1.7 Condition and Stability
Bibliographic Notes; Bibliography; Problems
Chapter 2. Approximation and Algorithms
2.1 Approximation
2.1-1 Classes of Approximating Functions; 2.1-2 Types of Approximations; 2.1-3 The Case for Polynomial Approximation
2.2 Numerical Algorithms