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Krylov Subspace Solvers and Preconditioners [PDF]
ESAIM: Proceedings and Surveys, 2018 In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved.
Vuik C.
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The Hamiltonian extended Krylov subspace method [PDF]
The Electronic Journal of Linear Algebra, 2022 An algorithm for constructing a $J$-orthogonal basis of the extended Krylov subspace$\mathcal{K}_{r,s}=\operatorname{range}\{u,Hu, H^2u,$ $ \ldots, $ $H^{2r-1}u, H^{-1}u, H^{-2}u, \ldots, H^{-2s}u\},$where $H \in \mathbb{R}^{2n \times 2n}$ is a large (and sparse) Hamiltonian matrix is derived (for $r = s+1$ or $r=s$).
Peter Benner +2 more
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Reduced-Rank Adaptive Filtering Using Krylov Subspace [PDF]
EURASIP Journal on Advances in Signal Processing, 2002 A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions ...
Burykh Sergueï, Abed-Meraim Karim
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Estimating the numerical range with a Krylov subspace
CoRRKrylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix. In contrast to prior results, which often depend on the gaps between eigenvalues, our estimates depend only on the ...
Cecilia Chen, John Urschel
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Krylov Subspace Estimation [PDF]
SIAM Journal on Scientific Computing, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael K. Schneider, Alan S. Willsky
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Preconditioners for Krylov subspace methods: An overview [PDF]
GAMM-Mitteilungen, 2020 AbstractWhen simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large‐scale systems of equations.
Pearson, John W., Pestana, Jennifer
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Pipelined, Flexible Krylov Subspace Methods [PDF]
SIAM Journal on Scientific Computing, 2016 We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with operator and nonlinear or nondeterministic preconditioner application.The methods are hence aimed at hiding network
Patrick Sanan +2 more
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Krylov Subspace Methods in Dynamical Sampling [PDF]
Sampling Theory in Signal and Image Processing, 2016 Let $B$ be an unknown linear evolution process on $\mathbb C^d\simeq l^2(\mathbb Z_d)$ driving an unknown initial state $x$ and producing the states $\{B^\ell x, \ell = 0,1,\ldots\}$ at different time levels. The problem under consideration in this paper is to find as much information as possible about $B$ and $x$ from the measurements $Y=\{x(i)$, $Bx ...
Akram Aldroubi, Ilya A. Krishtal
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Randomized Orthogonal Projection Methods for Krylov Subspace Solvers [PDF]
, 2023 Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce quasi-optimal ...
Timsit, Edouard +2 more
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KRYLOV SUBSPACE METHODS FOR SOLVING LARGE LYAPUNOV EQUATIONS [PDF]
, 1994 Published ...
KASENALLY, EM, JAIMOUKHA, IM
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