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Adaptively restarted block Krylov subspace methods with low-synchronization skeletons
With the recent realization of exascale performance by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like...
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Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods
Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in...
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On an integrated Krylov-ADI solver for large-scale Lyapunov equations
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear...
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A Krylov-Schur-like method for computing the best rank-(r1,r2,r3) approximation of large and sparse tensors
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have...
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Optimal size of the block in block GMRES on GPUs: computational model and experiments
The block version of GMRES (BGMRES) is most advantageous over the single right hand side (RHS) counterpart when the cost of communication is high...
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A study of defect-based error estimates for the Krylov approximation of φ-functions
Prior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential e t A v , is...
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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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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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Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side
Motivated by the effectiveness of Krylov projection methods and the CP decomposition of tensors, which is a low rank decomposition, we propose...
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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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Linearized Krylov subspace Bregman iteration with nonnegativity constraint
Bregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality of the...
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On Parallel Multigrid Methods for Solving Systems of Linear Algebraic Equations
In this paper, we consider algebraic multigrid methods (AMG) for solving symmetric positive-definite systems of linear algebraic equations (SLAE)...
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Parallel Methods for Solving Saddle Type Systems
Parallel methods for solving saddle-type algebraic systems that are relevant for modeling processes and phenomena in the problems of...
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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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On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems
The problem of shifted linear systems is an important and challenging issue in a number of research applications. Krylov subspace methods are...
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Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces
For computing the smallest eigenvalue and the corresponding eigenvector of a Hermitian matrix, by introducing a concept of perfect Krylov subspace,...
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The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients
This paper is mainly focused on the solution of Sylvester matrix differential equations with time-independent coefficients. We propose a new approach...
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The simpler block CMRH method for linear systems
The block changing minimal residual method based on the Hessenberg reduction algorithm (in short BCMRH) is a recent block Krylov method that can...
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Comparative Analysis of Parallel Methods for Solving SLAEs in Three-Dimensional Initial-Boundary Value Problems
Iterative methods for solving systems of linear algebraic equations with high-order sparse matrices that arise in absolutely stable implicit...
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Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis
In this paper, the block generalized product-type bi-conjugate gradient (GPBi-CG) method for solving large, sparse nonsymmetric linear systems of...
