An analysis of linear algebra algorithms with emphasis placed on both their mathematical analysis and practical applications. Totally examined by projects. Competence in Fortran or C is a prerequisite. Normally appropriate for Mathematics Year 4 and JMC 3.
Direct methods for linear systems: triangular equations, Gauss elimination, LU-decomposition, conditioning and finite-precision arithmetic, partial and complete pivoting, Cholesky factorisation, band matrices, QR-factorisation. Iterative methods for linear systems: Richardson, Jacobi, Gauss - Seidel, SOR; block variants; convergence criteria; Chebyshev acceleration. Symmetric eigenvalue problem: power method and variants, JacobiÕs method, Householder reduction to tridiagonal form, eigenvalues of tridiagonal matrices, the QR method. Krylov subspace methods: Lanczos method; conjugate gradient method, preconditioning. Introduction to multigrid.