Geodesic
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.
DOI : 10.21136/AM.1988.104283
Classification : 15A60, 65F30, 68Q25
Keywords: matrix power; matrix function; logarithmic computational complexity 
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     author = {Je\v{z}ek, Jan},
     title = {An efficient algorithm for computing real powers of a matrix and a related matrix function},
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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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