scholarly journals Corrigendum to “KIOPS: A fast adaptive Krylov subspace solver for exponential integrators” [J. Comput. Phys. 372 (2018) 236–255]

2021 ◽  
pp. 110443
Author(s):  
Stéphane Gaudreault ◽  
Greg Rainwater ◽  
Mayya Tokman
2018 ◽  
Vol 372 ◽  
pp. 236-255 ◽  
Author(s):  
Stéphane Gaudreault ◽  
Greg Rainwater ◽  
Mayya Tokman

2011 ◽  
Author(s):  
Isabelle G. Bajeux-Besnainou ◽  
Wachindra Bandara ◽  
Efstathia Bura

Author(s):  
Yuka Hashimoto ◽  
Takashi Nodera

AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.


2020 ◽  
Vol 28 (1) ◽  
pp. 15-32
Author(s):  
Silvia Gazzola ◽  
Paolo Novati

AbstractThis paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from discretizations of inverse ill-posed problems. The main idea underlying the new methods is to consider some rank-deficient approximations of the transpose of the system matrix, obtained by running the (transpose-free) Arnoldi algorithm, and then apply some Krylov solvers to a formally right-preconditioned system of equations. Theoretical insight is given, and many numerical tests show that the new solvers outperform classical Arnoldi-based or CG-like methods in a variety of situations.


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