| Title:
|
An efficient algorithm for computing real powers of a matrix and a related matrix function (English) |
| Author:
|
Ježek, Jan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1988 |
| Pages:
|
22-32 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
matrix power |
| Keyword:
|
matrix function |
| Keyword:
|
logarithmic computational complexity |
| MSC:
|
15A60 |
| MSC:
|
65F30 |
| MSC:
|
68Q25 |
| idZBL:
|
Zbl 0637.65036 |
| idMR:
|
MR0934371 |
| DOI:
|
10.21136/AM.1988.104283 |
| . |
| Date available:
|
2008-05-20T18:33:43Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104283 |
| . |
| Reference:
|
[1] F. R. Gantmacher: Theory of matrices.(in Russian). Moscow 1966. English translation: Chelsea, New York 1966. |
| Reference:
|
[2] B. Randell L. J. Russel: Algol 60 Implementation.Academic Press 1964. Russian translation: Mir 1967. MR 0215554 |
| Reference:
|
[3] D. E. Knuth: The art of computer programming, vol 2.Addison-Wesley 1969. Russian translation: Mir 1977. Zbl 0191.18001, MR 0633878 |
| Reference:
|
[4] J. Ježek: Computation of matrix exponential, square root and logarithm.(in Czech). Knižnica algoritmov, diel III, symposium Algoritmy, SVTS Bratislava 1975. |
| Reference:
|
[5] J.Ježek: General matrix power and sum of matrix powers.(in Czech). Knižnica algoritmov, diel IX, symposium Algoritmy, SVTS Bratislava 1987. |
| . |
