Prologue
P1 Overview
P2 Numerical Analysis Software
P3 Textbooks and Monographs
P3.1 Selected Textbooks on Numerical Analysis
P3.2 Monographs and Books on Specialized Topics
P4 Journals
1 Machine Arithmetic and Related Matters
1.1 Real Numbers, Machine Numbers, and Rounding
1.1.1 Real Numbers
1.1.2 Machine Numbers
1.1.3 Rounding
1.2 Machine Arithmetic
1.2.1 A Model of Machine Arithmetic
1.2.2 Error Propagation in Arithmetic Operations: Cancellation Error
1.3 The Condition of a Problem
1.3.1 Condition Numbers
1.3.2 Examples
1.4 The Condition of an Algorithm
1.5 Computer Solution of a Problem; Overall Error
1.6 Notes to Chapter 1
Exercises and Machine Assignments to Chapter 1
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
2 Approximation and Interpolation
2.1 Least Squares Approximation
2.1.1 Inner Products
2.1.2 The Normal Equations
2.1.3 Least Squares Error; Convergence
2.1.4 Examples of Orthogonal Systems
2.2 Polynomial Interpolation
2.2.1 Lagrange Interpolation Formula: Interpolation Operator
2.2.2 Interpolation Error
2.2.3 Convergence
2.2.4 Chebyshev Polynomials and Nodes
2.2.5 Barycentric Formula
2.2.6 Newton's Formula
2.2.7 Hermite Interpolation
2.2.8 Inverse Interpolation
2.3 Approximation and Interpolation by Spline Functions
2.3.1 Interpolation by Piecewise Linear Functions
2.3.2 A Basis for Sf (A)
2.3.3 Least Squares Approximation
2.3.4 Interpolation by Cubic Splines
2.3.5 Minimality Properties of Cubic Spline Interpolants
2.4 Notes to Chapter 2
Exercises and Machine Assignments to Chapter 2
Exercises
