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Tables of Contents for Numerical Linear Algebra
Chapter/Section Title
Page #
Page Count
Preface
ix
Acknowledgments
xi
I Fundamentals
1
38
Matrix-Vector Multiplication
3
8
Orthogonal Vectors and Matrices
11
6
Norms
17
8
The Singular Value Decomposition
25
7
More on the SVD
32
7
II QR Factorization and Least Squares
39
48
Projectors
41
7
QR Factorization
48
8
Gram-Schmidt Orthogonalization
56
7
MATLAB
63
6
Householder Triangularization
69
8
Least Squares Problems
77
10
III Conditioning and Stability
87
58
Conditioning and Condition Numbers
89
8
Floating Point Arithmetic
97
5
Stability
102
6
More on Stability
108
6
Stability of Householder Triangularization
114
7
Stability of Back Substitution
121
8
Conditioning of Least Squares Problems
129
8
Stability of Least Squares Algorithms
137
8
IV Systems of Equations
145
34
Gaussian Elimination
147
8
Pivoting
155
8
Stability of Gaussian Elimination
163
9
Cholesky Factorization
172
7
V Eigenvalues
179
62
Eigenvalue Problems
181
9
Overview of Eigenvalue Algorithms
190
6
Reduction to Hessenberg or Tridiagonal Form
196
6
Rayleigh Quotient, Inverse Iteration
202
9
QR Algorithm without Shifts
211
8
QR Algorithm with Shifts
219
6
Other Eigenvalue Algorithms
225
9
Computing the SVD
234
7
VI Iterative Methods
241
80
Overview of Iterative Methods
243
7
The Arnoldi Iteration
250
7
How Arnoldi Locates Eigenvalues
257
9
GMRES
266
10
The Lanczos Iteration
276
9
From Lanczos to Gauss Quadrature
285
8
Conjugate Gradients
293
10
Biorthogonalization Methods
303
10
Preconditioning
313
8
Appendix The Definition of Numerical Analysis
321
8
Notes
329
14
Bibliography
343
10
Index
353