Perturbations of the matrix logarithm

• Autorzy: Gil' M.
• Języki publikacji: EN

Abstrakty

EN

The paper suggests sharp norm estimates for the matrix logarithm and for the difference of the logarithms of two matrices.

Słowa kluczowe

EN

matrix logarithm; perturbations; norm estimates

PL

logarytm macierzy; perturbacje; szacowanie normy

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 1
• Strony: 47--68
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Gil' M.

• Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel,

Bibliografia

• [1] R. Bhatia, Matrix Analysis, Springer, New York, 1997.
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• [3] J. R. Cardoso and F. Silva Leite, Theoretical and numerical considerations about Pade approximants for the matrix logarithm, Linear Algebra Appl. 330 (2001), 31-42.
• [4] C. M. Carracedo and M. S. Alix, The Theory of Fractional Powers of Operators, Elsevier, Amsterdam, 2001.
• [5] Y. L. Daleckii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, American Mathematical Society, Providence, 1974.
• [6] A. O. Gel'fond, Calculations of Finite Differences (in Russian), Nauka, Moscow, 1967.
• [7] M. I. Gil', Operator Functions and Localization of Spectra, Lectures Notes in Math. 1830, Springer, Berlin, 2003.
• [8] M. I. Gil', Estimates for entries of matrix valued functions of infinite matrices. Math. Phys. Anal. Geom. 11 (2008), 175-186.
• [9] M. I. Gil', Perturbations of functions of operators in a Banach space. Math. Phys. Anal. Geom. 13 (2010), 69-82.
• [10] M. A. Krasnosel'skii, J. Lifshits and A. Sobolev. Positive Linear Systems. The Method of Positive Operators, Heldermann Verlag, Berlin, 1989.
• [11] N. Sherif and E. Morsy, Computing real logarithm of a real matrix, Int. J. Algebra 2 (2008), 131-142.
• [12] V. A. Yakubovich and V. M. Starzhinskii, Differential Equations with Periodic Coefficients, John Wiley, New York, 1975.