3 papers
math.NA2026
Theoretical insights on the residual transformation from bi-conjugate gradient into bi-conjugate residual via a smoothing scheme
Arisa Kawase, Kensuke Aihara
Bi-conjugate gradient (Bi-CG) and bi-conjugate residual (Bi-CR) methods are underlying iterative solvers for linear systems with nonsymmetric matrices. Residual smoothing is a stan…
math.NA2025
Transformation from Bi-CG into Bi-CR using a residual smoothing-like scheme
Arisa Kawase, Kensuke Aihara
Residual smoothing techniques, which produce a smooth convergence behavior of linear iterative solvers, also form connections between different methods. For example, minimal residu…
math.NA2024
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…