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Krylov Subspace Methods on Supercomputers [PDF]
SIAM Journal on Scientific and Statistical Computing, 1989 This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance.
Yousef Or Youcef Saad
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MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks
, 2014 We proposed MATEX, a distributed framework for transient simulation of power distribution networks (PDNs). MATEX utilizes matrix exponential kernel with Krylov subspace approximations to solve differential equations of linear circuit.
Cheng, Chung-Kuan +3 more
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Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined Conjugate Gradient method [PDF]
, 2017 Pipelined Krylov subspace methods typically offer improved strong scaling on parallel HPC hardware compared to standard Krylov subspace methods for large and sparse linear systems.
Agullo, Emmanuel +4 more
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Energies, 2020 In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature.
Ning Wang, Huifang Wang, Shiyou Yang
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Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques [PDF]
, 2013 In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework.
Isao Yamada +3 more
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Krylov SSP Integrating Factor Runge–Kutta WENO Methods
Mathematics, 2021 Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF ...
Shanqin Chen
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Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems
Abstract and Applied Analysis, 2014 Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented.
Cui-Xia Li, Yan-Jun Liang, Shi-Liang Wu
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Biorthogonal Extended Krylov Subspace Methods
, 2018 Extended Krylov subspace methods generalize classical Krylov, since also products with the inverse of the matrix under consideration are allowed. Recent advances have shown how to efficiently construct an orthogonal basis for the extended subspace, as well as how to build the highly structured projected matrix, named an extended Hessenberg matrix.
Van Buggenhout, Niel +2 more
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On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations
Mathematics, 2017 In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration ...
Abdeslem Hafid Bentbib +2 more
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Rosenbrock-Krylov Methods for Large Systems of Differential Equations
, 2014 This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or semi-discrete PDEs ...
Sandu, Adrian, Tranquilli, Paul
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