Objectif |

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. |

Descriptif |

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, ... |

Recommended courses |

Required : Linear algebra, multivariate calculus, numerical analysis. Advised : Some programming exposure in any of the following languages: Matlab, R, Python, Julia, ... |

Evaluation |

Oral exam and homework throughout the semester |

- Teacher: Ding Lu
- Teacher: Bart Vandereycken