16 citations · 27 across the 6 of their papers we have counts for
7 papers · 1 filter
Error control technique of quadrature-based algorithms for the action of real powers of a Hermitian positive-definite matrix
Motohiro Otsuka, Fuminori Tatsuoka, Tomohiro Sogabe +2
This study considers quadrature-based algorithms to compute , the action of a real power of a Hermitian positive-definite matrix on a vector $ \boldsymbol{b}…
An error control framework for computing the exponential of matrices arising from the finite element discretization
Fuminori Tatsuoka, Yuto Miyatake, Tomohiro Sogabe
Several methods for computing the action of the matrix exponential are expressed by substituting into a rational appro…
A preconditioning technique of Gauss--Legendre quadrature for the logarithm of symmetric positive definite matrices
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi +1
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 cond…
Computing the matrix exponential with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi +1
This paper considers the computation of the matrix exponential with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus…
Computing the matrix fractional power with the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +2
Two quadrature-based algorithms for computing the matrix fractional power are presented in this paper. These algorithms are based on the double exponential (DE) formula, whic…
Algorithms for the computation of the matrix logarithm based on the double exponential formula
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +1
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 form…
A cost-efficient variant of the incremental Newton iteration for the matrix th root
Fuminori Tatsuoka, Tomohiro Sogabe, Yuto Miyatake +1
Incremental Newton (IN) iteration, proposed by Iannazzo, is stable for computing the matrix th root, and its computational cost is flops per iteration. In th…