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- W2035240667 abstract "The Kreiss matrix theorem asserts three necessary and sufficient conditions for a family of matrices of fixed finite order to be L2-stable: a resolvent condition (R), a triangularization condition (S) and a Hermitian norm condition (H). We extend the Kreiss theorem to families of matrices of finite but unbounded order with the restriction that the degrees of the minimal polynomials of all matrices in the family are less than a fixed constant. For such matrix families, we show that (R) and (H) remain necessary and sufficient for L2-stability, while (S) must be replaced by a somewhat stronger “block triangularization” condition (S′). This extended Kreiss theorem permits a corresponding extension of the Buchanan stability theorem." @default.
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- W2035240667 date "1976-01-01" @default.
- W2035240667 modified "2023-10-16" @default.
- W2035240667 title "An extension of the Kreiss stability theorem to families of matrices of unbounded order" @default.
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- W2035240667 doi "https://doi.org/10.1016/0024-3795(76)90070-7" @default.
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