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An efficient algorithm for computing real powers of a matrix and a related matrix function
Applications of Mathematics, Tome 33 (1988) no. 1, pp. 22-32
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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.
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.
DOI : 10.21136/AM.1988.104283
Classification : 15A60, 65F30, 68Q25
Keywords: matrix power; matrix function; logarithmic computational complexity 
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Ježek, Jan. An efficient algorithm for computing real powers of a matrix and a related matrix function. Applications of Mathematics, Tome 33 (1988) no. 1, pp. 22-32. doi: 10.21136/AM.1988.104283

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[2] B. Randell L. J. Russel: Algol 60 Implementation. Academic Press 1964. Russian translation: Mir 1967. | MR

[3] D. E. Knuth: The art of computer programming, vol 2. Addison-Wesley 1969. Russian translation: Mir 1977. | MR | Zbl

[4] J. Ježek: Computation of matrix exponential, square root and logarithm. (in Czech). Knižnica algoritmov, diel III, symposium Algoritmy, SVTS Bratislava 1975.

[5] J.Ježek: General matrix power and sum of matrix powers. (in Czech). Knižnica algoritmov, diel IX, symposium Algoritmy, SVTS Bratislava 1987.

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