Power bounded and exponentially bounded matrices

Jaromír J. Koliha; Ivan Straškraba

Applications of Mathematics (1999)

  • Volume: 44, Issue: 4, page 289-308
  • ISSN: 0862-7940

Abstract

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The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.

How to cite

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Koliha, Jaromír J., and Straškraba, Ivan. "Power bounded and exponentially bounded matrices." Applications of Mathematics 44.4 (1999): 289-308. <http://eudml.org/doc/33035>.

@article{Koliha1999,
abstract = {The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.},
author = {Koliha, Jaromír J., Straškraba, Ivan},
journal = {Applications of Mathematics},
keywords = {power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour; power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour},
language = {eng},
number = {4},
pages = {289-308},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Power bounded and exponentially bounded matrices},
url = {http://eudml.org/doc/33035},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Koliha, Jaromír J.
AU - Straškraba, Ivan
TI - Power bounded and exponentially bounded matrices
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 4
SP - 289
EP - 308
AB - The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
LA - eng
KW - power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour; power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour
UR - http://eudml.org/doc/33035
ER -

References

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  1. Singular Systems of Differential Equations, Pitman, Boston, 1980. (1980) Zbl0419.34007
  2. Generalized Inverses of Linear Transformations, Surveys and Reference Works in Mathematics, Pitman, London, 1979. (1979) 
  3. Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964. (1964) Zbl0161.12101MR0175290
  4. 10.1090/S0273-0979-1982-15018-2, Bull. Amer. Math. Soc. 6 (1982), 463–465. (1982) MR0648536DOI10.1090/S0273-0979-1982-15018-2
  5. Matrix Analysis for Applied Sciences, volume 1, 2, Teubner-Texte zur Mathematik 60, 84, Teubner, Leipzig, 1983, 1986. (1983, 1986) MR0731071
  6. Applied Linear Algebra, 3rd edition, Prentice-Hall, Englewood Cliffs, 1988. (1988) MR0572995
  7. 10.1137/0131057, SIAM J. Appl. Math. 31 (1976), 646–648. (1976) Zbl0355.15008MR0422303DOI10.1137/0131057
  8. 10.1016/0024-3795(81)90006-9, Lin. Algebra Appl. 38 (1981), 33–49. (1981) Zbl0468.15002MR0636023DOI10.1016/0024-3795(81)90006-9
  9. 10.1137/1023036, SIAM Review 23 (1981), 143–164. (1981) Zbl0466.15005MR0618637DOI10.1137/1023036

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