Session II.3 - Real-Number Complexity
Poster
A geometric condition number for nonlinear underdetermined systems
Nick Dewaele
KU Leuven, Belgium - This email address is being protected from spambots. You need JavaScript enabled to view it.
The condition number of a system of equations $F(x,p) = 0$ parameterised by $p$ measures the sensitivity of the solution $x$ with respect to small changes in $p$. However, some systems admit infinitely many solutions $x$ for any given value of $p$, in which case the standard condition number is always infinite. This poster presents a generalised condition number (called the least-squares condition number) that is generically finite for many underdetermined systems and measures perturbations to the solution in a least-squares sense relative to some reference solution. The expression of this condition number in terms of the partial derivatives of $F$ relates it to existing work on complexity (Dedieu and Kim, 2002) and on distance to singularity (Dégot, 2001). The theory is applied to common matrix and tensor factorisations.
Joint work with Nick Vannieuwenhoven (KU Leuven, Belgium).