Upper bounds for singular values Original Research Article

Let A be an n × n matrix with singular values σ1 greater-or-equal, slanted cdots, three dots, centered greater-or-equal, slanted σn. If 1 less-than-or-equals, slant r less-than-or-equals, slant n, then σr=minHset membership, variantSrdouble vertical barHdouble vertical bar, where Sr is the set of n × n matrices H such that rank(A + H) less-than-or-equals, slant r − 1 and short parallel·short parallel denotes the spectral norm, i.e., the largest singular value. We find upper bounds for σr by choosing H suitably.