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Koliha, J. J.; Straškraba, I.

Power bounded and exponentially bounded matrices. (English) Zbl 1060.34506

Appl. Math., Praha 44, No. 4, 289-308 (1999).
The authors prove spectral decompositions for the power and exponentially bounded matrices and apply these results to obtain series and integral representations of the Drazin inverse and to describe the asymptotic behaviour of solutions of linear ordinary differential equations, including the singular and singularly perturbed ones. An example of localized travelling waves for a system of conservation laws is given. In the proofs a new characterization of eigenprojections obtained in the paper is utilized.
Reviewer: Milan Tvrdý (Praha)

Cited in 4 Documents

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
15A09 Theory of matrix inversion and generalized inverses
34E15 Singular perturbations for ordinary differential equations
39A11 Stability of difference equations (MSC2000)

Keywords:

power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour
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\textit{J. J. Koliha} and \textit{I. Straškraba}, Appl. Math., Praha 44, No. 4, 289--308 (1999; Zbl 1060.34506)
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References:

[1] S. L. Campbell: Singular Systems of Differential Equations. Pitman, Boston, 1980. · Zbl 0419.34007
[2] S. L. Campbell and C. D. Meyer: Generalized Inverses of Linear Transformations. Surveys and Reference Works in Mathematics, Pitman, London, 1979.
[3] A. S. Householder: Theory of Matrices in Numerical Analysis. Blaisdell, New York, 1964. · Zbl 0161.12101
[4] Tai-Ping Liu: Resonance for quasilinear hyperbolic equation. Bull. Amer. Math. Soc. 6 (1982), 463-465. · Zbl 0501.76048
[5] I. Marek and K. Žitný: Matrix Analysis for Applied Sciences, volume 1, 2. Teubner-Texte zur Mathematik 60, 84, Teubner, Leipzig, 1983, 1986.
[6] B. Noble and J. W. Daniel: Applied Linear Algebra, 3rd edition. Prentice-Hall, Englewood Cliffs, 1988. · Zbl 0413.15002
[7] U. G. Rothblum: A representation of the Drazin inverse and characterizations of the index. SIAM J. Appl. Math. 31 (1976), 646-648. · Zbl 0355.15008
[8] U. G. Rothblum: Resolvent expansions of matrices and applications. Lin. Algebra Appl. 38 (1981), 33-49. · Zbl 0468.15002
[9] U. G. Rothblum: Expansions of sums of matrix powers. SIAM Review 23 (1981), 143-164. · Zbl 0466.15005
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