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An efficient algorithm for computing real power of a matrix and a related matrix function. (English) Zbl 0637.65036
The algorithm proposed to compute A r and (A \(r-1)(A-1)^{-1}\), for a square matrix A and a real r, uses the binary expansion of r and has the logarithmic computational complexity with respect to r. The main idea is to reduce it by cumulating computations; the same idea has been applied previously for r integer and not just for matrices [cf. D. E. Knuth, The art of computer programming, II (1969; Zbl 0191.180)].
Reviewer: A.de Castro
65F30 Other matrix algorithms (MSC2010)
68Q25 Analysis of algorithms and problem complexity
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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