An efficient algorithm for computing real powers of a matrix and a related matrix function

Jan Ježek

Aplikace matematiky (1988)

  • Volume: 33, Issue: 1, page 22-32
  • ISSN: 0862-7940

Abstract

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The paper is devoted to an algorithm for computing matrices A r and ( A r - I ) . ( A - I ) - 1 for a given square matrix A and a real r . The algorithm uses the binary expansion of r and has the logarithmic computational complexity with respect to r . The problem stems from the control theory.

How to cite

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Ježek, Jan. "An efficient algorithm for computing real powers of a matrix and a related matrix function." Aplikace matematiky 33.1 (1988): 22-32. <http://eudml.org/doc/15520>.

@article{Ježek1988,
abstract = {The paper is devoted to an algorithm for computing matrices $A^r$ and $(A^r -I).(A-I)^\{-1\}$ for a given square matrix $A$ and a real $r$. The algorithm uses the binary expansion of $r$ and has the logarithmic computational complexity with respect to $r$. The problem stems from the control theory.},
author = {Ježek, Jan},
journal = {Aplikace matematiky},
keywords = {matrix power; matrix function; logarithmic computational complexity; matrix power; matrix function; logarithmic computational complexity},
language = {eng},
number = {1},
pages = {22-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An efficient algorithm for computing real powers of a matrix and a related matrix function},
url = {http://eudml.org/doc/15520},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Ježek, Jan
TI - An efficient algorithm for computing real powers of a matrix and a related matrix function
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 1
SP - 22
EP - 32
AB - The paper is devoted to an algorithm for computing matrices $A^r$ and $(A^r -I).(A-I)^{-1}$ for a given square matrix $A$ and a real $r$. The algorithm uses the binary expansion of $r$ and has the logarithmic computational complexity with respect to $r$. The problem stems from the control theory.
LA - eng
KW - matrix power; matrix function; logarithmic computational complexity; matrix power; matrix function; logarithmic computational complexity
UR - http://eudml.org/doc/15520
ER -

References

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  1. F. R. Gantmacher, Theory of matrices, (in Russian). Moscow 1966. English translation: Chelsea, New York 1966. (1966) Zbl0136.00410
  2. B. Randell L. J. Russel, Algol 60 Implementation, Academic Press 1964. Russian translation: Mir 1967. (1964) Zbl0115.12702MR0215554
  3. D. E. Knuth, The art of computer programming, vol 2, Addison-Wesley 1969. Russian translation: Mir 1977. (1969) Zbl0191.18001MR0633878
  4. J. Ježek, Computation of matrix exponential, square root and logarithm, (in Czech). Knižnica algoritmov, diel III, symposium Algoritmy, SVTS Bratislava 1975. (1975) 
  5. J.Ježek, General matrix power and sum of matrix powers, (in Czech). Knižnica algoritmov, diel IX, symposium Algoritmy, SVTS Bratislava 1987. (1987) 

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