12 citations · 59 across the 16 of their papers we have counts for
16 papers
Block cross-interactive residual smoothing for Lanczos-type solvers for linear systems with multiple right-hand sides
Kensuke Aihara, Akira Imakura, Keiichi Morikuni
Lanczos-type solvers for large sparse linear systems often exhibit large oscillations in the residual norms. In finite precision arithmetic, large oscillations increase the residua…
Complex moment-based methods for differential eigenvalue problems
Akira Imakura, Keiichi Morikuni, Akitoshi Takayasu
This paper considers computing partial eigenpairs of differential eigenvalue problems (DEPs) such that eigenvalues are in a certain region on the complex plane. Recently, based on…
Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh$\unicode{x2013}$Ritz procedure for generalized Hermitian eigenvalue problems
Akira Imakura, Keiichi Morikuni, Akitoshi Takayasu
We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses compl…
GMRES Methods for Tomographic Reconstruction with an Unmatched Back Projector
Per Christian Hansen, Ken Hayami, Keiichi Morikuni
Unmatched pairs of forward and back projectors are common in X-ray CT computations for large-scale problems; they are caused by the need for fast algorithms that best utilize the c…
Cross-interactive residual smoothing for global and block Lanczos-type solvers for linear systems with multiple right-hand sides
Kensuke Aihara, Akira Imakura, Keiichi Morikuni
Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solve…
A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations
Zeyu Liao, Ken Hayami, Keiichi Morikuni +1
Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining the minimum-norm solution of inconsistent underdetermined systems of linear equations. Morikuni (Ph.D. thesis…
Projection method for eigenvalue problems of linear nonsquare matrix pencils
Keiichi Morikuni
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil…
Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems
Yi-Shu Du, Ken Hayami, Ning Zheng +2
We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a pa…
Shifted Lanczos method for quadratic forms with Hermitian matrix resolvents
Keiichi Morikuni
Quadratic forms of Hermitian matrix resolvents involve the solutions of shifted linear systems. Efficient iterative solutions use the shift-invariance property of Krylov subspaces…
Multiclass spectral feature scaling method for dimensionality reduction
Momo Matsuda, Keiichi Morikuni, Akira Imakura +2
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information…
Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems
Akira Imakura, Keiichi Morikuni, Akitoshi Takayasu
We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral-type eigensolv…
Spectral feature scaling method for supervised dimensionality reduction
Momo Matsuda, Keiichi Morikuni, Tetsuya Sakurai
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the…
On GMRES for singular EP and GP systems
Keiichi Morikuni, Miroslav Rozložník
In this contribution, we study the numerical behavior of the Generalized Minimal Residual (GMRES) method for solving singular linear systems. It is known that GMRES determines a le…
Implementation of Interior-point Methods for LP based on Krylov Subspace Iterative Solvers with Inner-iteration Preconditioning
Yiran Cui, Keiichi Morikuni, Takashi Tsuchiya +1
We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed…
Multistep matrix splitting iteration preconditioning for singular linear systems
Keiichi Morikuni
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized min…
Inner-iteration preconditioning with a symmetric splitting matrix for rank-deficient least squares problems
Keiichi Morikuni
Stationary iterative methods with a symmetric splitting matrix are performed as inner-iteration preconditioning for Krylov subspace methods. We give conditions such that the inner-…