Bounds for the Singular Values of a Matrix
Alan Jennings · IMA Journal of Numerical Analysis · 1982
A lower-bound theorem is developed for the singular values of a matrix A (and therefore for the eigenvalues of B = AHA). It is found that there is always a unique column scaling of A which produces the optimum bound. However, sharper bounds still may sometimes be obtained by taking advantage of matrix partitioning. It is shown that the resulting bounds may often (but not always) be better than those obtained by applying Gerschgorin's theorem to B. The equivalent upper-bound theorem is found to be weak.