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Further lower bounds for the smallest singular value. (English) Zbl 0891.15013
The authors derive three better lower bounds for the smallest singular value of a general complex matrix, using three variants of Gershgorin’s theorem. Three new bounds are non-comparable and involve more complicated expressions, but generally larger lower bounds.
Reviewer: P.Narain (Bombay)

MSC:
15A42 Inequalities involving eigenvalues and eigenvectors
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References:
[1] Gudkov, V.V., On a certain test for nonsingularity of matrices, (), 385-390, (MR 33, 1967, No. 1323)
[2] Horn, R.; Johnson, C.R., Matrix analysis, (1985), Cambridge U.P Cambridge · Zbl 0576.15001
[3] Horn, R.; Johnson, C.R., Topics in matrix analysis, (1991), Cambridge U.P New York · Zbl 0729.15001
[4] Johnson, C.R., A gersgorin-type lower bound for the smallest singular value, Linear algebra appl., 112, 1-7, (1989) · Zbl 0723.15013
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