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Session III.1 - Numerical Linear Algebra

Wednesday, June 21, 17:00 ~ 17:30

What part of a numerical problem is ill-conditioned?

Nick Dewaele

KU Leuven, Belgium   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many numerical problems with input $x$ and output $y$ can be formulated as an system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this numerical problem, one can derive a (typically underdetermined) subproblem by omitting any number of constraints from $F$. We propose a condition number for underdetermined systems that relates the condition number of a numerical problem to those of its subproblems. We illustrate the use of our technique by computing the condition of two numerical linear algebra problems that do not have a condition number in the classical sense: the decomposition of a low-rank matrix into unstructured factors and Tucker decomposition.

Joint work with Nick Vannieuwenhoven (KU Leuven, Belgium).

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