The corse is suitable for those students who have had a first introductory course on numerical methods but have not yet been exposed to systematic courses on Numerical Linear Algebra and Optimization.
Part I, Computational Methods of Linear Algebra
Review of basic facts from linear algebra.
Stability and conditioning in Numerical Linear Algebra.
Matrix Factorizations (LU, Cholesky, QR...).
Direct and Iterative methods for solving linear systems.
Computation of eigenvalues and eigenvector of matrices.
Least squares problems, the Moore-Penrose pseudoinverse, singular value decomposition.
Part II, Methods of Numerical Optimization
-Gradient descent, Newton and Quasi-Newton methods.
-Method of Lagrange multipliers, augmented Lagrangian methods.
The goal of this course is to provide the students the basic tools of numerical linear algebra and of optimization (both constrained and unconstrained).
The emphasis will be on the fundamental concepts (in particular those of stability and conditioning of problems) and on the algorithmic aspects.
References will be provided in the course of the lectures.