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Showing 1 to 20 of 38 for “"Lanczos"”.
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Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB
… of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS …
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New Remedial Approaches to the Breakdown of Lanczos-type Algorithms
… one of the best known iterative schemes is the Lanczos algorithm. It has however, a very serious shortcoming in that it break down frequently before achieving convergence to an acceptable solution. This project focuses on investigating this breakdown issue. There are a number of attempts to …
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Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.
… versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the …
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A utilização de vetores de Lanczos-Ritz na condensação dinâmica de estruturas
… and the substructure representation by its Lanczos-Ritz vectors were implemented. A correction in the substructure base of transformation through an iterative process was proposed in order to obtain a correct modal representation of inertia forces.
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Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method
… The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a formal error analysis which relates the errors to …
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Enhanced Lanczos Algorithms for Solving Systems of Linear Equations with Embedding Interpolation and Extrapolation
Lanczos-type algorithms are prone to breaking down before convergence to an acceptable solution is achieved. This study investigates a number of ways to deal with this issue. In the first instance, we investigate the quality of three types of restarting points in the restarting strategy when …
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Estudo sobre a qualidade da resposta dinâmica do Método de Superposição dos Modos de Lanczos
… a study about a dynamic response quality for Lanczos Mode Superposition Method for structures submitted to large range of excitation periods is carried out. The unbalanced equation of motion, or residual, was evaluated from global parameters to address the response quality of a modal …
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Análise estática não-linear geométrica de estruturas pelo método de superposição modal com base Lanczos-Ritz
… vectors produced in a non-iterative way from a Lanczos algorithm. In the method of buckling mode superposition the eingenvectores have been tradionally used as basis vectors. The high computational cost of this procedure, caused by the iterative character of the eingenvalue problem, is its main …
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A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Multiprocessor sparse SVD algorithms and applications
… of the sparse symmetric eigenvalue problem using Lanczos (with or without re-orthogonalization) and subspace iteration methods. Our intent is to extend and refine this knowledge for computing the sparse singular value decomposition on a parallel computer. We emphasize Lanczos, block-Lanczos, …
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Multilevel solution procedures for structural dynamics eigenvalue problems
… into the subspace iteration and block Lanczos methods to produce implicit subspace and Lanczos multigrid methods. The nested iteration technique is adopted to produce the initial trial vectors. Second, the basic multigrid idea of fine mesh relaxation followed by a coarse mesh correction …
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Recycling Krylov Subspaces and Preconditioners
… Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual linear systems may have application-specific advantages. For example, using BiCG to solve the dual linear systems arising in interpolatory model reduction provides a backward error …
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Fast algorithms for Brownian dynamics simulation with hydrodynamic interactions
… have considered several methods: the classical Lanczos method, the Chebyshev-Davidson method, and the safeguarded Lanczos method proposed by Zhou and Li [7]. Our numerical experiments indicate that K is usually very small when the particles are distributed uniformly with low density, and that …
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Krylov Projection Methods for Model Reduction
… projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a …
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A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors
… show that block GMRES and the new block Radau-Lanczos method can be regarded as modified BFOM. In analogy to Sh-BFOM(m), we develop an efficient restart procedure for shifted BGMRES with restarts (Sh-BGMRES(m)), as well as error bounds. Using this framework and shifted block Krylov methods with …
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Convergence of the Arnoldi Iteration for Estimating Extreme Eigenvalues
… of work proving gap-independent bounds for the Lanczos method, which depend only on the matrix dimensions and number of iterations, to the more general Arnoldi case.
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Integração direta da resposta em regime permanente pelo Método de Ritz-Wilson com mudança de base
… mode superposition method as well as the Lanczos method are briefly reviewed and a set of numerical examples are presented and discussed.
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A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators
… problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated.
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Unrolling of Graph Total Variation for Image Denoising
… implementation, this response is realized by Lanczos approximation. This method outperformed DnCNN by up to 3dB in PSNR in statistical mistmatch case.
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An Adaptive Approach to Gibbs’ Phenomenon
… rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was …
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