Suppose we aim to solve a system Ax = b where the matrix A is square and full rank. Then, as we know from linear algebra, it has a unique solution given by x* = A^{-1}b. However, as soon as we allow rectangular or rank deficient matrices in the left hand side, the problem becomes more interesting. For example, when the system is overdetermined and exact solution does not exist, we could search for "the best" approximation for the solution by solving an optimization (so-called, least-squares) problem, and if the system is underdetermined and there are multiple solutions, we could search for "the best" solution among them. In this class, we will formalize what could "the best" mean in the previous sentence, and discuss several (direct and iterative) optimization-based methods for solving linear systems.
Solving linear systems: optimization perspective
20.01.2021 17:00 - 17:20
Organiser:
Fakultät für Mathematik
Location:
Online via Zoom