ISSN:
1572-9125
Keywords:
primary 39A11
;
secondary 15A45, 30A10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Kreiss Matrix Theorem asserts the uniform equivalence over allN ×N matrices of power boundedness and a certain resolvent estimate. We show that the ratio of the constants in these two conditions grows linearly withN, and we obtain the optimal proportionality factor up to a factor of 2. Analogous results are also given for the related problem involving matrix exponentialse 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01934916
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