Preface |
Fundamental: / Part I: |
Matrix-vector multiplication / 1: |
Orthogonal vectors and matrices / 2: |
Norms / 3: |
The singular value decomposition / 4: |
More on the SVD / 5: |
QR Factorization and Least Squares: / Part II: |
Projectors / 6: |
QR factorization / 7: |
Gram-Schmidt orthogonalization / 8: |
MATLAB / 9: |
Householder triangularization / 10: |
Least squares problems / 11: |
Conditioning and Stability: / Part III: |
Conditioning and condition numbers / 12: |
Floating point arithmetic / 13: |
Stability / 14: |
More on stability / 15: |
Stability of householder triangularization / 16: |
Stability of back substitution / 17: |
Conditioning of least squares problems / 18: |
Stability of least squares algorithms / 19: |
Systems of Equations: / Part IV: |
Gaussian elimination / 20: |
Pivoting / 21: |
Stability of Gaussian elimination / 22: |
Cholesky factorization / 23: |
Eigenvalues: / Part V: |
Eigenvalue problems / 24: |
Overview of Eigenvalue algorithms / 25: |
Reduction to Hessenberg or tridiagonal form / 26: |
Rayleigh quotient, inverse iteration / 27: |
QR algorithm without shifts / 28: |
QR algorithm with shifts / 29: |
Other Eigenvalue algorithms / 30: |
Computing the SVD / 31: |
Iterative Methods: / Part VI: |
Overview of iterative methods / 32: |
The Arnoldi iteration / 33: |
How Arnoldi locates Eigenvalues / 34: |
GMRES / 35: |
The Lanczos iteration / 36: |
From Lanczos to Gauss quadrature / 37: |
Conjugate gradients / 38: |
Biorthogonalization methods / 39: |
Preconditioning / 40: |
Appendix |
Notes |
Bibliography |
Index |
Preface |
Fundamental: / Part I: |
Matrix-vector multiplication / 1: |
Orthogonal vectors and matrices / 2: |
Norms / 3: |
The singular value decomposition / 4: |