Table of Contents

Chapter 1. Power Tools of the Trade

1.1 Vectors and Plotting

1.2 More Vectors, More Plotting, and Now Matrices

1.3 Building Exploratory Environments

1.4 Error

1.5 Designing Functions

1.6 Structure Arrays and Cell Arrays

1.7 More Refined Graphics

 

Chapter 2. Polynomial Interpolation

2.1 The Vandermonde Approach

2.2 The Newton Representation

2.3 Properties

2.4 Special Topics

 

Chapter 3. Piecewise Polynomial Interpolation

3.1 Piecewise Linear Interpolation

3.2 Piecewise Cubic Hermite Interpolation

3.3 Cubic Splines

 

Chapter 4. Numerical Integration

4.1 The Newton-Cotes Rules

4.2 Composite Rules

4.3 Adaptive Quadrature

4.4 Special Topics

4.5 Shared Memory Adaptive Quadrature

 

Chapter 5. Matrix Computations

5.1 Setting Up Matrix Problems

5.2 Matrix Operations

5.3 Once Again, Setting Up Matrix Problems

5.4 Recursive Matrix Operations

5.5 Distributed Memory Matrix Multiplication

 

Chapter 6. Linear Systems

6.1 Triangular Problems

6.2 Banded Problems

6.3 Full Problems

6.4 Analysis

 

Chapter 7. The QR and Cholesky Factorizations

7.1 Least Squares Fitting

7.2 The QR factorization

7.3 The Cholesky Factorization

7.4 High-Performance Cholesky

 

Chapter 8. Nonlinear Equations and Optimization

8.1 Finding Roots

8.2 Minimizing a Function of One Variable

8.3 Minimizing Multivariate Functions

8.4 Solving Systems of Nonlinear Equations

 

Chapter 9. The Initial Value Problem

9.1 Basic Concepts

9.2 The Runge-Kutta Methods

9.3 The Adams Methods