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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Krylov subspace split Bregman methods
Applied Numerical Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Majed Alotaibi +2 more
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Sampling Error Analysis in Quantum Krylov Subspace Diagonalization [PDF]
QuantumQuantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where limited quantum circuit depth is available. In contrast to the classical Krylov subspace diagonalization
Gwonhak Lee, Dongkeun Lee, Joonsuk Huh
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Krylov subspace approximations for the exponential Euler method: error estimates and the harmonic Ritz approximant [PDF]
, 2011 We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method ...
Carr, Elliot, Ilic, Milos, Turner, Ian
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A Geometric Multigrid Method for 3D Magnetotelluric Forward Modeling Using Finite-Element Method
Remote Sensing, 2023 The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency.
Xianyang Huang +8 more
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Convergence rates for inverse-free rational approximation of matrix functions [PDF]
, 2016 This article deduces geometric convergence rates for approximating matrix functions via inverse-free rational Krylov methods. In applications one frequently encounters matrix functions such as the matrix exponential or matrix logarithm; often the matrix ...
Jagels, Carl +3 more
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Extending quasi-GMRES method to solve generalized Sylvester tensor equations via the Einstein product [PDF]
Iranian Journal of Numerical Analysis and OptimizationThis paper aims to extend a Krylov subspace technique based on an in-complete orthogonalization of Krylov tensors (as a multidimensional exten-sion of the common Krylov vectors) to solve generalized Sylvester tensor equations via the Einstein product ...
M.M. Izadkhah
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Biorthogonal rational Krylov subspace methods [PDF]
ETNA - Electronic Transactions on Numerical Analysis, 2019 Summary: A general framework for oblique projections of non-Hermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured pencil, where the structure can take several forms such as ...
Van Buggenhout, Niel +2 more
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A framework for deflated and augmented Krylov subspace methods [PDF]
, 2013 We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems.
André Gaul +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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