OPERATION COUNTS
7.4 THE FACTORIZATION
7.5 PERTURBATION, CONDITIONING AND STABILITY
7.6 SPD MATRICES AND THE CHOLESKY DECOMPOSITION
7.7 APPLICATION: NUMERICAL SOLUTION OF LINEAR LEAST SQUARES PROBLEMS
7.8 SPARSE AND STRUCTURED MATRICES
7.9 ITERATIVE METHODS FOR LINEAR SYSTEMS – A BRIEF SURVEY
7.10 NONLINEAR SYSTEMS: NEWTON'S METHOD AND RELATED IDEAS
7.11 APPLICATION: NUMERICAL SOLUTION OF NONLINEAR BVP's
12 CHAPTER 8: APPROXIMATE SOLUTION OF THE ALGEBRAIC EIGENVALUE PROBLEM 8.1 EIGENVALUE REVIEW 8.2 REDUCTION TO HESSENBERG FORM 8.3 POWER METHODS 8.4 BISECTION AND INERTIA TO COMPUTE EIGENVALUES OF SYMMETRIC MATRICES 8.5 AN OVERVIEW OF THE ITERATION 8.6 APPLICATION: ROOTS OF POLYNOMIALS, II 8.7 APPLICATION: COMPUTATION OF GAUSSIAN QUADRATURE RULES NOTE
13 CHAPTER 9: A SURVEY OF NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 9.1 DIFFERENCE METHODS FOR THE DIFFUSION EQUATION 9.2 FINITE ELEMENT METHODS FOR THE DIFFUSION EQUATION 9.3 DIFFERENCE METHODS FOR POISSON EQUATIONS NOTE
14 CHAPTER 10: AN INTRODUCTION TO SPECTRAL METHODS 10.1 SPECTRAL METHODS FOR TWO‐POINT BOUNDARY VALUE PROBLEMS 10.2 SPECTRAL METHODS IN TWO DIMENSIONS 10.3 SPECTRAL METHODS FOR TIME‐DEPENDENT PROBLEMS 10.4 CLENSHAW‐CURTIS QUADRATURE
List of Tables
1 Chapter 2Table 2.1 Derivative Approximations.Table 2.2 Table for Problem 4.Table 2.3 (Table 2.1 in text.) Example of derivative approximation to
2 Chapter 3Table 3.1 Solutions to Problem 3.1.3Table 3.2 Solutions to Problem 3.1.10.Table 3.3 Solution to Problem 3.2.11.Table 3.4 Solutions to Problem 3.3.3.Table 3.5 Newton iteration for Problem 4d, §3.4.Table 3.6 Data for Problems 3 and 4.Table 3.7 Newton iteration for
3 Chapter 4Table 4.1 Data for Problem 7.Table 4.2 Data for Problem 8.Table 4.3 Table of
4 Chapter 5Table 5.1 Data for Problem 6.Table 5.2 Results for Exercise 5.3.6.Table 5.3 Results for Exercise 5.4.7.Table 5.4 Data for Problem 10.Table 5.5 Table of
5 Chapter 6Table 6.1 Solutions to Exercise 6.2.4.Table 6.2 Results for Problem 8, first part.Table 6.3 Results for Problem 8, second part.
6 Chapter 7Table 7.1 Random vector tests (Problem 3), using Problem 2(d).Table 7.2 Data for Problem 7.
7 Chapter 9Table 9.1 Results for Problem 4.Table 9.2 Results for Problem 5.
8 Chapter 10Table 10.1 Spectral solution results for Problem 10.2.3.Table 10.2 Solution for 10.3.2(b) and (c).
List of Illustrations
1 Chapter 2Figure 2.1 Exact solution for Exercise 2.3.7.Figure 2.2 Error plot for Exercise 2.3.7.Figure 2.3 Exact solution for Exercise 2.3.9.Figure 2.4 Error plot for Exercise 2.3.9.Figure 2.5 Estimated timing cost for Problem 13, semilog scale.Figure 2.6 Exact solution for Exercise 2.7.8.
2 Chapter 3Figure 3.1 Solution for Problem 3.2.7.Figure 3.2 Orbital geometry for Problems 4 and 5Figure 3.3 Solution for Problem 3.8.10.Figure 3.4 Solution curves for Problem 5, using 20 points.Figure 3.5 Solution
