Maha Hassanein

MTH 741 Numerical Linear Algebra
Pre-requisite: MTH 414 , MTH 601 or equivalent

Floating-point representation – Round-off error and error  propagation – Direct methods for linear equations – kronecker product and Sylvester equation – Matrix preconditioning schemes – Nearness to singularity – Ill-conditioning and condition number – A-priori and A-posteriori bounds – Wilkinson's iterative refinement – Interval methods and the Oettli-Prager criterion – Stability of numerical solutions and the backward error – Iterative methods: Jacobi, Gauss-Seidel, Relaxation – Rate of convergence – Parallelism for sparse matrices – Algebraic eigenvalue problem –
QR and SVD decompositions – Power method – Inverse iteration - LU factorization and their block version - Krylov subspace methods for solving linear systems (GMRES) and for solving eigenproblem (Lanczos); Rate of convergence.