Numerical mathematics and scientific computation

Contents......Page 1
Introduction......Page 9
Gaussion Elimination and LU Factorization......Page 10
Banded Systems......Page 31
Symmetric Matrices......Page 36
Block Matrix Algorithms......Page 50
Direct Methods for General Sparse Systems......Page 62
Perturbation Theory and Error Analysis......Page 72
Structured Systems......Page 91
Introduction......Page 99
The Method of Normal Equations......Page 107
Least Squares and the SVD......Page 116
Gram-Schmidt Orthogonalization......Page 129
Orthogonal Factorizations......Page 137
Rank Deficient and Ill-Posed Problems......Page 153
Modified Least Squares Problems......Page 168
Some Generalized Problems......Page 178
Basic Properties......Page 197
Canonical Forms and Matrix Functions......Page 207
Perturbation Theory and Eigenvalue Bounds......Page 223
Jacobi Methods......Page 237
The Power Method......Page 244
Transformation to Condensed Form......Page 254
The LR and QR Algorithms......Page 265
Subspace Methods for Large Eigenvalue Problems......Page 286
Generalized Eigenvalue Problems......Page 298
Classical Iterative Methods......Page 311
Stationary Iterative Methods......Page 316
Successive Overrelaxation Methods......Page 326
Convergence Acceleration......Page 335
Projection Methods......Page 340
Krylov Subspace Methods......Page 346
Nonsymmetric Problems......Page 355
Preconditioned Iterative Methods......Page 370
Preconitioners......Page 375
Systems of Nonlinear Equations......Page 389
Unconstrained Optimization......Page 408
Nonlinear Least Squares Problems......Page 414
Constrained Linear Optimization......Page 431
Appendix: Calculus in Vector Space......Page 447
Appendix. Guide to Literature in Linear Algebra......Page 459
Index......Page 464
Initial Value Problems for ODEs Theoretical Background......Page 474
Control of Step Size and Numerical Stability......Page 500
One step Methods......Page 527
Linear Multistep Methods......Page 540
Extrapolation Methods......Page 553
Second Order Equations and Boundary Problems......Page 559
Qualitative Theory of ODEs......Page 574
General Concepts and Theorems for ODEs......Page 598
Introduction......Page 624
Partial Differential Equations......Page 627
Variational Methods......Page 639
Integral Equations......Page 645
15. Guide to Literature and Software......Page 650