2018
DOI: 10.1137/16m1073315
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Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector

Abstract: Abstract. We investigate different approaches for the computation of the action of the weighted geometric mean of two large-scale positive definite matrices on a vector. We derive several algorithms, based on numerical quadrature and the Krylov subspace, and compare them in terms of convergence speed and execution time. By exploiting an algebraic relation between the weighted geometric mean and its inverse, we show how these methods can be used for the solution of large linear system whose coefficient matrix i… Show more

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Cited by 19 publications
(23 citation statements)
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“…which is obtained by applying ( ) = (1 − ) /(1 + ) to (1). Integral representations similar to (28) are considered in [2,7]. In [7], under the assumption that max min = 1, the error of the GJ2 is estimated 1 to be…”
Section: Comparison Of the Convergence Speedmentioning
confidence: 99%
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“…which is obtained by applying ( ) = (1 − ) /(1 + ) to (1). Integral representations similar to (28) are considered in [2,7]. In [7], under the assumption that max min = 1, the error of the GJ2 is estimated 1 to be…”
Section: Comparison Of the Convergence Speedmentioning
confidence: 99%
“…It is known that uniquely exists when all the eigenvalues of lie in the set { ∈ C : ∉ (−∞, 0]}; see, e.g., [10]. The matrix fractional power arises in several situations of computational science, e.g., fractional differential equations [2,4,15], lattice QCD calculation [3], and computation of the weighted matrix geometric mean [7].…”
Section: Introductionmentioning
confidence: 99%
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