Results 11 to 20 of about 12,661,880 (175)
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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The Hamiltonian extended Krylov subspace method
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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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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Fractal and Fractional, 2023 Fractional derivatives and regime-switching models are widely used in various fields of finance because they can describe the nonlocal properties of the solutions and the changes in the market status, respectively.
Xu Chen +3 more
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A Preconditioned Fast Collocation Method for a Linear Nonlocal Diffusion Model in Convex Domains
IEEE Access, 2020 Recently, there are many papers dedicated to develop fast numerical methods for nonlocal diffusion and peridynamic models. However, these methods require the physical domain where we solve the governing equations is rectangular. To relax this restriction,
Xuhao Zhang, Aijie Cheng, Hong Wang
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On the Preconditioned Delayed Weighted Gradient Method
Trends in Computational and Applied Mathematics, 2023 In this article a preconditioned version of the Delayed Weighted Gradient Method (DWGM) is presented and analyzed. In addition to the convergence, some nice properties as the A- orthogonality of the current transformed gradient with all the previous ...
R. Aleixo, H. Lara Urdaneta
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Toeplitz-like preconditioner for linear systems from spatial fractional diffusion equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 The article deals with constructing Toeplitz-like preconditioner for linear systems arising from finite difference discretization of the spatial fractional diffusion equations. The coefficient matrices of these linear systems have an $S+L$ structure,
N. Akhoundi
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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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Flexible Krylov Methods for Edge Enhancement in Imaging
Journal of Imaging, 2021 Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non ...
Silvia Gazzola +2 more
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Measurement-efficient quantum Krylov subspace diagonalisation [PDF]
QuantumThe Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing.
Zongkang Zhang +3 more
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