## View abstract

### 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. document.getElementById('cloakc3cbd0ee7238929faba297a1a27644f2').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc3cbd0ee7238929faba297a1a27644f2 = 'n&#105;ck.d&#101;w&#97;&#101;l&#101;' + '&#64;'; addyc3cbd0ee7238929faba297a1a27644f2 = addyc3cbd0ee7238929faba297a1a27644f2 + 'k&#117;l&#101;&#117;v&#101;n' + '&#46;' + 'b&#101;'; var addy_textc3cbd0ee7238929faba297a1a27644f2 = 'n&#105;ck.d&#101;w&#97;&#101;l&#101;' + '&#64;' + 'k&#117;l&#101;&#117;v&#101;n' + '&#46;' + 'b&#101;';document.getElementById('cloakc3cbd0ee7238929faba297a1a27644f2').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc3cbd0ee7238929faba297a1a27644f2 + '\'>'+addy_textc3cbd0ee7238929faba297a1a27644f2+'<\/a>';

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).