Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities (Q1902063)
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scientific article; zbMATH DE number 815811
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities |
scientific article; zbMATH DE number 815811 |
Statements
Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities (English)
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1 April 1996
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It is shown how the resolvent conditions in the Kreiss matrix theorem [see \textit{H.-O. Kreiss}, BIT 2, 153-181 (1962; Zbl 0109.347)] for \(e^{tA}\) and \(A^\nu\), respectively, can be reformulated as certain strengthened Cauchy-Schwarz inequalities to be satisfied for all pairs \(w\), \(Aw\) \((w\in \mathbb{C}^n)\). This yields certain generalizations of the notions ``logarithmic norm'' and ``numerical radius'', respectively.
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logarithmic norm
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numerical radius
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resolvent conditions
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Kreiss matrix theorem
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Cauchy-Schwarz inequalities
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0.9395265
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0.9272131
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0.90452343
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0.9043447
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0.8878892
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0.88194615
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0.8796891
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