Bounds for norms of the matrix inverse and the smallest singular value (Q952048)
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scientific article; zbMATH DE number 5362062
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounds for norms of the matrix inverse and the smallest singular value |
scientific article; zbMATH DE number 5362062 |
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Bounds for norms of the matrix inverse and the smallest singular value (English)
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6 November 2008
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In the first part of the paper, some lower bounds for \(\| A^{-1}\| \) for \(M\)- and \(H\)-matrices are given. Here \(\| \cdot\| \) denotes an arbitrary matrix norm. However the main results of the papers are related to upper bounds for \(\| A^{-1}\| _{1}\) and \(\| A^{-1}\| _{\infty}\), where \(A\) is a strictly diagonally dominant matrix. As a consequence of these results some bounds for the smallest singular value are obtained.
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\(M\)-matrices
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diagonal dominance
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matrix norms
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singular values
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lower bounds
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\(H\)-matrices
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upper bounds
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0.9380479
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0.9340169
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0.93311656
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0.92648333
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0.91662496
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0.91543984
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0.91326785
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