Linear algebra is fundamental in many fields in mathematics and applied sciences. This course introduces the numerical techniques needed to solve a few of the classic problems in linear algebra but suitable in a large-sale setting. The focus will be on the mathematical analysis of the resulting algorithms.
1. Fundamentals: subspaces, orthogonality, rank, projectors, QR, LU, ' Examples of large-scale problems.
2. Eigenvalue problems: power and subspace iteration, Krylov methods, perturbation analysis.
3. Singular value decomposition and low-rank approximations, PCA.
4. Advanced topics (tentative): matrix functions, nonlinear eigenvalue problems, low-rank tensor methods, ...
Required : Linear algebra, multivariate calculus, numerical analysis. Advised : Some programming exposure in any of the following languages: Matlab, R, Python, Julia, ...
Oral exam and homework throughout the semester