On some stability bounds subject to Hille-Yosida resolvent conditions (Q1914874)
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scientific article; zbMATH DE number 885559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some stability bounds subject to Hille-Yosida resolvent conditions |
scientific article; zbMATH DE number 885559 |
Statements
On some stability bounds subject to Hille-Yosida resolvent conditions (English)
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14 November 1996
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Under certain assumptions on the matrix \(A\) and on the stability function \(\varphi(z)\) of a one-step method, the matrix \(B= \varphi(hA)\) is proved to satisfy the so-called Hille-Yosida resolvent condition. Using this result, it is shown that some of the bounds for the norm of the \(n\)th power of the matrix \(B\), recently proved by \textit{M. N. Spijker} and \textit{F. A. J. Straetemans} [Linear Algebra Appl. 239, 77-102 (1996)], are sharp.
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numerical stability
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stability function
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one-step method
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Hille-Yosida resolvent condition
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