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Keywords:
matrix power; matrix function; logarithmic computational complexity
matrix power; matrix function; logarithmic computational complexity
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.
References:
[1] F. R. Gantmacher: Theory of matrices. (in Russian). Moscow 1966. English translation: Chelsea, New York 1966.
[2] B. Randell L. J. Russel: Algol 60 Implementation. Academic Press 1964. Russian translation: Mir 1967. MR 0215554
[3] D. E. Knuth: The art of computer programming, vol 2. Addison-Wesley 1969. Russian translation: Mir 1977. MR 0633878 | Zbl 0191.18001
[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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