The structured distance to ill-posedness for conic systems

Details The structured distance to ill-posedness for conic systems The structured distance to ill-posedness for conic systems

2003-09-05

arxiv.org/abs/math/0309100v1

Mathematics

Optimization and Control

16 pages

Scientific paper

An important measure of conditioning of a conic linear system is the size of
the smallest structured perturbation making the system ill-posed. We show that
this measure is unchanged if we restrict to perturbations of low rank. We
thereby derive a broad generalization of the classical Eckart-Young result
characterizing the distance to ill-posedness for a linear map.

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