In an earlier paper of the first author, Gersgorin's theorem was used in a novel way to give a simple lower bound for the smallest singular value of a general complex matrix. That lower bound was stronger than previous published bounds. Here, we use three variants of Gersgorin's theorem in a similar
Further bounds for the smallest singular value and the spectral condition number
β Scribed by O. Rojo
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 541 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0898-1221
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β¦ Synopsis
We derive monotonic sequences of bounds for the extreme singular values. In particular, we find further lower bounds for the smallest singular value which improve the bounds of Yu and Gun. Also, we give new upper bounds for the spectral condition number. ~
π SIMILAR VOLUMES
In the first part, we obtain two easily calculable lower bounds for A -1 , where β’ is an arbitrary matrix norm, in the case when A is an M-matrix, using first row sums and then column sums. Using those results, we obtain the characterization of M-matrices whose inverses are stochastic matrices. With
We derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix. We also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegati