Estimation of \(\| A^{-1}\| _\infty \) for weakly chained diagonally dominant \(M\)-matrices (Q1044561)
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scientific article; zbMATH DE number 5650004
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimation of \(\| A^{-1}\| _\infty \) for weakly chained diagonally dominant \(M\)-matrices |
scientific article; zbMATH DE number 5650004 |
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Estimation of \(\| A^{-1}\| _\infty \) for weakly chained diagonally dominant \(M\)-matrices (English)
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18 December 2009
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Let \(A\) be a weakly chained diagonally dominant \(M\)-matrix. In this paper, a new upper bound for \(\| A^{-1}\| _\infty \) is presented. This bound is applied to establish a lower bound for the smallest eigenvalue of \(A\). The effectiveness of the upper bound is shown numerically with two examples.
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weakly chained diagonally dominant matrix
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\(M\)-matrix
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norm
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numerical examples
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smallest eigenvalue
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upper bound
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