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Randomized flexible GMRES with deflated restarting
For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We...
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A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs
In this work, we propose a simple yet generic preconditioned Krylov subspace method for a large class of nonsymmetric block Toeplitz all-at-once...
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Robustness and Accuracy in Pipelined Bi-conjugate Gradient Stabilized Methods
In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to...
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The global Golub-Kahan method and Gauss quadrature for tensor function approximation
This paper is concerned with Krylov subspace methods based on the tensor t-product for computing certain quantities associated with generalized...
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GCGE: a package for solving large scale eigenvalue problems by parallel block dam** inverse power method
In this paper, we introduce some strategies to improve the efficiency and scalability of the generalized conjugate gradient algorithm and build a...
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Learning Linearized Assignment Flows for Image Labeling
We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows for image labeling. An exact formula is derived for...
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Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations
Based on the finite-difference method, the considered Riesz space-fractional diffusion equations result in a series of linear systems, whose...
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Application of an extrapolation method in the Hessenberg algorithm for computing PageRank
PageRank can be viewed as a hyperlink-based method for estimating the importance of nodes in a network, and has attracted a lot of attention from...
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Multi-parameter dimensional split preconditioner for three-by-three block system of linear equations
For a class of three-by-three block systems of linear equations arising from many practical problems, we develop a multi-parameter dimensional split...
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Hybrid Parallel ILU Preconditioner in Linear Solver Library GaspiLS
Krylov subspace solvers such as GMRES and preconditioners such as incomplete LU (ILU) are the most commonly used methods to solve general-purpose,...
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Preconditioned Krylov subspace and GMRHSS iteration methods for solving the nonsymmetric saddle point problems
In the present paper, we propose a separate approach as a new strategy to solve the saddle point problem arising from the stochastic Galerkin finite...
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Interpretation of parareal as a two-level additive Schwarz in time preconditioner and its acceleration with GMRES
We describe an interpretation of parareal as a two-level additive Schwarz preconditioner in the time domain. We show that this two-level...
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A posteriori error bounds for the block-Lanczos method for matrix function approximation
We extend the error bounds from Chen et al. ( SIAM J. Matrix Anal. Appl 43(2):787–811,
2022 ) for the Lanczos method for matrix function approximation...
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SimSky: An Accuracy-Aware Algorithm for Single-Source SimRank Search
SimRank is a popular node-pair similarity search model based on graph topology. It has received sustained attention due to its wide range of...
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Exact inverse solution techniques for a class of complex valued block two-by-two linear systems
By taking a complex factorization of the Schur complement matrix into consideration, we present practical expressions for the inverses of a class of...
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Alya toward exascale: algorithmic scalability using PSCToolkit
In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and...
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Parallel Combined Chebyshev and Least Squares Iterations in the Krylov Subspaces
The combined Chebyshev−Least Squares iterative processes in the Krylov subspaces to solve symmetric and non-symmetric systems of linear algebraic...
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A sign-based linear method for horizontal linear complementarity problems
For the horizontal linear complementarity problem, we establish a linear method based on the sign patterns of the solution of the equivalent modulus...
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Estimating error norms in CG-like algorithms for least-squares and least-norm problems
In Meurant et al. (Numer. Algorithms 88 (3), 1337–1359,
2021 ), we presented an adaptive estimate for the energy norm of the error in the conjugate...
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New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization
In this paper, two new subspace minimization conjugate gradient methods based on p -regularization models are proposed, where a special scaled norm in p ...
