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1 Finite precision arithmetic, errors, condition of a problem
2 Stability of algorithms, calculating with machine numbers
3 Vector and matrix spaces, vector and matrix norms
4 Linear equation systems
5 Gauss elimination, pivoting, LU decomposition
6 Cholesky decomposition, Givens rotations, banded matrices
7 Eigenvalue problem, Jacobi and Power methods
8 Gram-Schmidt orthogonalization, QR algorithm
9 Iterative methods for linear equation systems and error analysis
10 Jacobi, Gauss-Seidel and SOR methods
11 Non-stationary iterative methods
12 Krylov subspace methods and Conjugate Gradient method
13 GMRES methods
14 Preconditioning and its applications |