Numerical matrix computations

Lecturer: Timo Eirola
Teaching assistant: Armando W. Gutiérrez

This is a six-week graduate-level course designed for students with a major in mathematics, applied mathematics, physics, mechanics, and computer science. The student learns to analyse and solve problems in linear algebra that occur often in scientific computing, data fitting and optimisation. The course focuses on solutions of linear systems, least squares problems, eigenvalue problems, and stability of numerical methods.

Content:

• Matrix decompositions and their numerical computation
• Eigenvalue iterations
• Sparse matrices
• Iterative methods for solving linear systems
• LU decomposition, Cholesky decomposition, QR decomposition and Givens rotations
• Perturbation analysis
• Fixed-point iteration
• Line search methods
• Gradient descent algorithm
• Orthogonal projections and Krylov subspaces

Study material:

• Golub, G.H. and Van Loan C.F. Matrix computations (3rd edition). John Hopkins University Press, 1996
• Trefethen, L.N. and Bau, D. Numerical linear algebra (1st edition). SIAM, 1997