Minimizing the Condition Number for Small Rank Modifications
Chen Greif, J. M. Varah · SIAM Journal on Matrix Analysis and Applications · 2006
We consider the problem of minimizing the condition number of a low rank modification of a matrix. Analytical results show that the minimum, which is not necessarily unique, can be obtained and expressed by a small number of eigenpairs or singular pairs. The symmetric and the nonsymmetric cases are analyzed, and numerical experiments illustrate the analytical observations.