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MSc in Mathematical Modelling & Scientific Computing MSc in Applied and Computational Mathematics |
16 lectures MT 2003 Dr A J Wathen |
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, multigrid.
Approximation theory, Chebyshev semi-iterative methods, conjugate gradients, convergence analysis using approximation theory. Preconditioning.
Reading List
L N Trefethen and D Bau III, Numerical Linear Algebra, SIAM, 1997
A Greenbaum, Iterative Solution Methods for Linear Systems, SIAM, 1997
O Axelsson and V A Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic Press, 1984
G H Golub and C F van Loan, Matrix Computations, John Hopkins University Press, 3rd edition, 1996
M J D Powell, Approximation Theory and Methods, CUP, 1981
R S Varga, Matrix Iterative Analysis, Prentice Hall, 1962, (Sections 3.1 and 5.1) out of print
W L Briggs, A Multigrid Tutorial, SIAM, 1987, Chs. 1,2 and 3
or
W L Briggs, V E Henson & S F McCormick, A multigrid Tutorial (2nd edition), SIAM 2000 (Chapter 1, 2 and 3)