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

Aplikace matematiky (1988)

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

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topJežek, 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

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