| 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： |
