Syllabus
1. Methods for solving symmetric linear systems of equations - Lanczos method, SYMMLQ, MINRES.
2. Methods for solving nonsymmetric linear systems of equations based on orthogonality and long recurrences - FOM, GMRES.
3. Methods for solving nonsymmetric linear systems of equations based on biorthogonality and short recurrences - CGS, BiCG, BiCGstab, QMR, TFQMR.
4. Methods connected with normal equations - CGLS, LSQR.
5. Block methods.
6. Idea of preconditioning.
7. Convergence and numerical stability - comparison and examples.
Annotation
The course is devoted to the most widely used Krylov subspace iterative methods for solving systems of linear algebraic equations, linear approximation problems and eigenvalue problems. The emphasis is put especially on effective algorithmic realization and convergence analysis.
The course extends some topics discussed in the course Analysis of Matrix
Calculations 1 (NMNM331).