Matrix factorizations. Perturbation and error analysis. Operation cost and convergence rate. Direct Methods for linear systems. LU and Cholesky factorizations. Perturbation and error analysis. Vector and matrix norms. Perturbation analysis for linear systems. Error analysis. Classical iterative methods. Jacobi and Gauss-Seidel method. Convergence analysis. SOR method. Krylov subspace methods. Steepest descent method. Conjugate gradient method. Practical CG method and convergence analysis. Preconditioning. GMRES method.

MATB122
MATB211