2010
DOI: 10.1007/s11075-009-9357-1
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A binary powering Schur algorithm for computing primary matrix roots

Abstract: An algorithm for computing primary roots of a nonsingular matrix A is presented. In particular, it computes the principal root of a real matrix having no nonpositive real eigenvalues, using real arithmetic. The algorithm is based on the Schur decomposition of A and has an order of complexity lower than the customary Schur based algorithm, namely the Smith algorithm.

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Cited by 17 publications
(12 citation statements)
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“…To show c k,i < 0 for k ≥ 2 and i ≥ 1, we only need to show that c 2,i < 0 for i ≥ 1. By (7) and (12)…”
Section: Sign Pattern Of Coefficients C Ki In Power Series Expansionsmentioning
confidence: 86%
“…To show c k,i < 0 for k ≥ 2 and i ≥ 1, we only need to show that c 2,i < 0 for i ≥ 1. By (7) and (12)…”
Section: Sign Pattern Of Coefficients C Ki In Power Series Expansionsmentioning
confidence: 86%
“…In previous work [11,16], we have shown that, for the kth root, the computational cost of the straightforward algorithm [22] can be reduced by considering substitution algorithms that exploit more efficient matrix powering schemes. However, a fraction can be evaluated in several different ways, and some approaches require fewer matrix multiplications than applying Horner's method twice.…”
Section: Discussionmentioning
confidence: 99%
“…When T ∈ C N ×N is upper triangular, the blocks along the diagonal of T are of size 1 × 1 and ν = N . Equation (11) involves just scalars and can be written as ψ ij y ij = ϕ ij , where…”
Section: Complex Schur Formmentioning
confidence: 99%
See 1 more Smart Citation
“…For example Smith [2003], Guo and Higham [2006], Greco and Iannazzo [2010], and Iannazzo and Manasse [2013] have all used the identity X p − A = 0 to assess algorithms for computing matrix pth roots. The identity e log A = A has been used by Davies and Higham [2003] and Dieci et al [1996] to test algorithms for the matrix logarithm.…”
Section: Introductionmentioning
confidence: 99%