Results 31 to 40 of about 81,041 (236)
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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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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Krylov Subspace Methods in Dynamical Sampling [PDF]
Sampling Theory in Signal and Image Processing, 2016 12 pages, 2 ...
Aldroubi, Akram, Krishtal, Ilya
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Randomized Orthogonal Projection Methods for Krylov Subspace Solvers [PDF]
arXiv.org, 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 ...
E. Timsit, L. Grigori, O. Balabanov
semanticscholar +1 more source
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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Quantum Power Method by a Superposition of Time-Evolved States
PRX Quantum, 2021 We propose a quantum-classical hybrid algorithm of the power method, here dubbed as the quantum power method, to evaluate H[over ^]^{n}|ψ⟩ with quantum computers, where n is a non-negative integer, H[over ^] is a time-independent Hamiltonian of interest,
Kazuhiro Seki, Seiji Yunoki
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A nested Krylov subspace method to compute the sign function of large complex matrices [PDF]
, 2011 We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density.
Bloch +22 more
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Solving Coupled Cluster Equations by the Newton Krylov Method
Frontiers in Chemistry, 2020 We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude.
Chao Yang +4 more
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On Numerical Approximations of the Koopman Operator
Mathematics, 2022 We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis.
Igor Mezić
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