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Showing 1 to 14 of 14 for “"Lanczos algorithm"”.
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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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Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method
Two algorithms of use in sparse matrix computation are studied. 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 …
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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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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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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 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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A geometric analysis of model reduction of linear systems
… particularly the reduction of structures via the Lanczos algorithm.
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Recycling Krylov Subspaces and Preconditioners
… or a sequence of dual linear systems. We develop algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate …
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New Remedial Approaches to the Breakdown of Lanczos-type Algorithms
There are numerous algorithms for the solution of systems of linear equations and eigenvalue problems. Among such methods, 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 …
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Computational Approaches to the Nuclear Many-Body Problem
… costs. In this research, I augment the block Lanczos algorithm using a <em>bootstrapped</em> pivot to significantly reduce the number of Hamiltonian-matrix multiplications typically dominating the algorithm’s total time-to-solution. My results demonstrate significant speedup in …
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Uncertainty quantification in ocean state estimation
… scalable matrix-free numerical linear algebra algorithms. Hessian-vector product and Jacobian derivative codes of the MIT general circulation model (MITgcm) are generated by means of algorithmic differentiation (AD). Computational complexity of the Hessian code is reduced by tangent linear …
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Uncertainty Quantification in ocean state estimation
… scalable matrix-free numerical linear algebra algorithms. Hessian-vector product and Jacobian derivative codes of the MIT general circulation model (MITgcm) are generated by means of algorithmic differentiation (AD). Computational complexity of the Hessian code is reduced by tangent linear …
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Nuevas herramientas software para el diseño de dispositivos pasivos de microondas basadas en elementos finitos 3D y redes neuronales
… eficientemente aplicando el algoritmo de Lanczos al modelo de elementos finitos de las regiones. Finalmente, se presentan diversos ejemplos en los que se ilustran las capacidades de los métodos que se presentan. Primero se obtienen modelos de regiones pequeñas de dispositivos pasivos de …
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Efficient Finite Element Electromagnetic Analysis for High-Frequency/High-Speed Circuits And Multiconductor Transmission Lines
This dissertation comprises the following four components. (1) Development of a robust and efficient 3-D finite element electromagnetic field solver with high-order vector elements for high-frequency and high-speed circuit simulations. The solver supports wave port and lumped port excitations as …