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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…