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Inexact Krylov Subspace Methods for Linear Systems [PDF]
SIAM Journal on Matrix Analysis and Applications, 2004 This paper is devoted to the impact of perturbations of the matrix-vector product in various Krylov subspace solvers. This problem is related to the rounding errors analysis of Krylov subspace methods since in the latter case an inexact matrix-vector product is one source of errors.
Eshof, J. van den, Sleijpen, G.L.G.
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S-Step BiCGStab Algorithms for Geoscience Dynamic Simulations
Oil & Gas Science and Technology, 2016 In basin and reservoir simulations, the most expensive and time consuming phase is solving systems of linear equations using Krylov subspace methods such as BiCGStab.
Anciaux-Sedrakian Ani +3 more
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Preserving Symmetry in Preconditioned Krylov Subspace Methods [PDF]
SIAM Journal on Scientific Computing, 1998 The authors consider the problem of solving linear systems of equations with coefficient matrices which are ``nearly'' (very close to be) symmetric and when symmetric positive definite preconditioners are used. They show that it is possible to improve upon the standard practice of using nonsymmetric preconditioners for that matrices along with a left ...
Tony F. Chan +3 more
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Enlarged Krylov Subspace Conjugate Gradient Methods for Reducing Communication [PDF]
, 2016 International audienceIn this paper we introduce a new approach for reducing communication in Krylov subspace methods that consists of enlarging the Krylov subspace by a maximum of $t$ vectors per iteration, based on a domain decomposition of the graph ...
Moufawad, Sophie +2 more
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Performance of relaxed iterative methods for image deblurring problems
Journal of Algorithms & Computational Technology, 2019 In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms.
Jae H Yun
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Krylov Subspace Methods in the Electronic Industry [PDF]
, 2006 In most practical cases, the convergence of the GMRES method applied to a linear algebraic system Ax -- b is determined by the distribution of eigenvalues of A. In theory, however, the information about the eigenvalues alone is not sufficient for determining the convergence. In this paper the previous work of Greenbaum et al.
Heres, P.J., Schilders, W.H.A.
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Extended block Hessenberg method for large-scale Sylvester differential matrix equations [PDF]
Journal of Mahani Mathematical ResearchIn this paper, we consider large-scale low-rank Sylvester differential matrix equations. We present two iterative methods for the approximate solution of such differential matrix equations. In the first method, exploiting the extended block Krylov method,
Azita Tajaddini
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High Voltage, EarlyView.ABSTRACT Structural mechanics field simulation plays a critical role in the vibration characteristic analysis of electrical equipment. Existing structural field analysis of equipment based on numerical simulation faces challenges such as convergence difficulties and prolonged computational time, failing to meet the demand for real‐time prediction of ...
Wanqing Wang +6 more
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Sparse Regularization Least-Squares Reverse Time Migration Based on the Krylov Subspace Method
Remote SensingLeast-squares reverse time migration (LSRTM) is an advanced seismic imaging technique that reconstructs subsurface models by minimizing the residuals between simulated and observed data. Mathematically, the LSRTM inversion of the sub-surface reflectivity
Guangshuai Peng +4 more
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Solid Mechanics Segregated Solver Acceleration With Jacobian‐Free Newton‐Krylov
International Journal for Numerical Methods in Engineering, Volume 127, Issue 11, 15 June 2026.ABSTRACT The segregated algorithm is a common approach for finite volumes solvers in solid mechanics, providing a memory‐efficient and straightforward implementation. Due to the inter‐coupling of the components through the source terms, it suffers from a slow convergence behavior in specific scenarios, such as geometries with significantly uneven ...
Andry Monlon +5 more
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