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A bound on powers of linear operators, with relevance to numerical stability

✍ Scribed by N. Borovykh; D. Drissi; M.N. Spijker

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 447 KB
Volume: 15
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(01)00091-x

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✦ Synopsis

In this note, we formulate a theorem giving bounds on the powers of linear operators, in a general Banach space setting. The relevance of the theorem is illustrated by applying it to the Crank-Nicholson method for the numerical solution of the heat equation. This application yields a stability estimate in the maximum norm which amounts to an improvement over a well-known result of Serdjukova [l].

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