On the Resolvent Condition I in the Kreiss
نویسندگان
چکیده
Abstrac t . The Kreiss Matrix Theorem asserts the uniform equivalence over all N x N matrices of power boundedness and a certain resolvent estimate. We show that the ratio of the constants in these two conditions grows linearly with N, and we obtain the optimal proportionality factor up to a factor of 2. Analogous results are also given for the related problem involving matrix exponentials e At. The proofs make use of a lemma that may be of independent interest, which bounds the arc length of the image of a circle in the complex plane under a rational function.
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تاریخ انتشار 1984