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Least Squares Methods in Krylov Subspaces
Journal of Mathematical Sciences, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Krylov Subspace Method Using Quantum Computing
2021The Krylov subspace algorithm uses iterative methods to solve bulky linear equations. It has a time complexity of O(n2) when run on a classical computing machine. The proposed algorithm has an exponential speedup over the classical algorithm. It takes O(n√k) time complexity when run on a quantum computer, where k is the condition number. In this paper,
Vidushi Jain, Yogesh Nagor
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A Krylov Subspace Method for Information Retrieval
SIAM Journal on Matrix Analysis and Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Blom, Katarina, Ruhe, Axel
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Convergence analysis of Krylov subspace methods
GAMM-Mitteilungen, 2004AbstractOne of the most powerful tools for solving large and sparse systems of linear algebraic equations is a class of iterative methods called Krylov subspace methods. Their significant advantages like low memory requirements and good approximation properties make them very popular, and they are widely used in applications throughout science and ...
Liesen, Jörg, Tichý, Petr
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Practical Implementation of Krylov Subspace Spectral Methods
Journal of Scientific Computing, 2007Krylov subspace spectral methods have been shown to be high-order accurate in time and more stable than time-stepping methods but also more difficult for an efficient implementation. The author shows how these methods should be used in practical solvers by exploiting the simple structure of differential operators.
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Extrapolation methods as nonlinear Krylov subspace methods
Linear Algebra and its ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Conor McCoid, Martin J. Gander
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Biconjugate direction methods in Krylov subspaces
Journal of Applied and Industrial Mathematics, 2010Summary: The paper addresses the orthogonal and variational properties of a family of iterative algorithms in Krylov subspaces for solving systems of linear algebraic equations with sparse nonsymmetric matrices. A biconjugate residual method, a squared biconjugate residual method, and a stabilized conjugate residual method are proposed and studied ...
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Krylov Subspace Methods for the Eigenproblem
2010These papers comprise some of Stewart’s recent contributions to the development and analysis of iterative algorithms based on Krylov subspace methods for computing eigenvalues.
Howard C. Elman, Dianne P. O’Leary
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A novel reduced-order algorithm for rational models based on Arnoldi process and Krylov subspace
Automatica, 2021Jing Chen, Biao Huang, Min Gan
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