Numerical Linear Algebra

Synopsis

Common problems in linear algebra. Matrix structure, singular value decomposition. QR factorization, the QR algorithm for eigenvalues. Direct solution methods for linear systems, Gaussian elimination and its variants. Iterative solution methods for linear systems.

Chebyshev polynomials and Chebyshev semi-iterative methods, conjugate gradients, convergence analysis, preconditioning. Preconditioning.

Reading List

• L N Trefethen and D Bau III, Numerical Linear Algebra, SIAM, 1997

• J W Demmel, Applied Numerial Linear Algebra, SIAM, 1997

• A Greenbaum, Iterative Methods for solving Linear Systems,, SIAM, 1997

• G H Golub and C F van Loan, Matrix Computations, John Hopkins University Press, 3rd edition, 1996

• H C Elman, D J Silvester and A J Wathen, Finite Elements and Fast Iterative Solvers, OUP, 1995 (only chapter 2)