GLORIA

GEOMAR Library Ocean Research Information Access

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • 1980-1984  (2)
Document type
Keywords
Publisher
Years
Year
  • 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
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 1-13 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the difference equations obtained when a linear multistep method is applied to the scalar test equationdy/dt=λy and constant stepsizeh. LetS be the region of the absolute stability of the method, and letD be a closed subset ofS (on the Riemann sphere $$\mathbb{C}$$ ). It is shown that the solutions of these difference equations are bounded forn≧0, uniformly for λh∈D.S is itself closed in $$\mathbb{C}$$ iff ∂S is free of cusps. The question is studed by means of contractivity analysis and a matrix theorem, derived from the matrix theorem of Kreiss.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400914
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...