2003/09/05 by Lewis, Adrian S.
#15A12 #65F35 #90C31 #93B35 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.math/0309100
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.