Výsledky vyhledávání - "Tatsuoka, Fuminori"

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A preconditioning technique of Gauss--Legendre quadrature for the logarithm of symmetric positive definite matrices

Autor: Tatsuoka, Fuminori, Sogabe, Tomohiro, Kemmochi, Tomoya, Zhang, Shao-Liang

This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss--Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a

Externí odkaz: http://arxiv.org/abs/2410.22014

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Akademický článek

Computing the matrix exponential with the double exponential formula

Autor: Tatsuoka Fuminori, Sogabe Tomohiro, Kemmochi Tomoya, Zhang Shao-Liang

Publikováno v: Special Matrices, Vol 12, Iss 1, Pp 970-989 (2024)

This article considers the computation of the matrix exponential eA{{\rm{e}}}^{A} with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian

Externí odkaz: https://doaj.org/article/7c76cdb981cc4f7fa61c7c9f9fead7b9

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Computing the matrix exponential with the double exponential formula

Autor: Tatsuoka, Fuminori, Sogabe, Tomohiro, Kemmochi, Tomoya, Zhang, Shao-Liang

Publikováno v: Spec. Matrices, 12 (2024) 20240013

This paper considers the computation of the matrix exponential $\mathrm{e}^A$ with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian mat

Externí odkaz: http://arxiv.org/abs/2306.14197

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Computing the matrix fractional power with the double exponential formula

Autor: Tatsuoka, Fuminori, Sogabe, Tomohiro, Miyatake, Yuto, Kemmochi, Tomoya, Zhang, Shao-Liang

Publikováno v: Electron. T. Numer. Ana., 54 (2021) 558-580

Two quadrature-based algorithms for computing the matrix fractional power $A^\alpha$ are presented in this paper. These algorithms are based on the double exponential (DE) formula, which is well-known for its effectiveness in computing improper integ

Externí odkaz: http://arxiv.org/abs/2012.01667

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Algorithms for the computation of the matrix logarithm based on the double exponential formula

Autor: Tatsuoka, Fuminori, Sogabe, Tomohiro, Miyatake, Yuto, Zhang, Shao-Liang

We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally employed;

Externí odkaz: http://arxiv.org/abs/1901.07834

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A cost-efficient variant of the incremental Newton iteration for the matrix $p$th root

Autor: Tatsuoka, Fuminori, Sogabe, Tomohiro, Miyatake, Yuto, Zhang, Shao-Liang

Publikováno v: J. Math. Res. Appl., 37 (2017), 107-118

Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix $p$th root, and its computational cost is $\mathcal{O}(n^3p)$ flops per iteration. In this paper, a cost-efficient variant of IN iteration is presented. The c

Externí odkaz: http://arxiv.org/abs/1611.02848

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