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  • 1
    Electronic Resource
    Electronic Resource
    On the resolvent condition in the Kreiss Matrix Theorem (1984)
    Springer
    BIT 24 (1984), S. 584-591 
    Details
    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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