Results 11 to 20 of about 1,908 (194)
An Arnoldi Method for Nonlinear Eigenvalue Problems [PDF]
BIT Numerical Mathematics, 2004 For the nonlinear eigenvalue problem T(lambda)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is
H. Voss, Voss, Heinrich
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On restarting the tensor infinite Arnoldi method [PDF]
BIT Numerical Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giampaolo Mele, Elias Jarlebring
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Augmented Block Householder Arnoldi Method
Linear Algebra and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baglama, James, James Baglama
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Arnoldi–Tikhonov regularization methods
Journal of Computational and Applied Mathematics, 2009 The problem is to solve a large, ill-conditioned linear system \(Ax=b\) of size \(n\), where \(b=\hat{b}+e\) with \(\hat{b}\) the ``true'' vector and \(e\) some error. Tikhonov regularization minimizes \(\|Ax-b\|^2+\mu^{-1}\|x\|\) with \(\mu\) a regularization parameter.
Lewis, Bryan, Reichel, Lothar
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A Block Arnoldi Method for the SPN Equations [PDF]
International Journal of Computer Mathematics, 2019 This work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P, MTM2017-85669-P and BES-2015-072901.
Antoni Vidal-Ferràndiz +3 more
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The influence of orthogonality on the Arnoldi method
Linear Algebra and its Applications, 2000 Error bounds for five orthogonalization methods and the Arnoldi method are summarized. It is shown that quality of the eigensolvers depends on the orthonormality of the computed basis. It is also shown that the stopping criterion based on the backward error and the value computed using the Arnoldi method can differ because of the loss of orthonormality
Braconnier, T. +2 more
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On restarting the Arnoldi method for large nonsymmetric eigenvalue problems [PDF]
Mathematics of Computation, 1996 The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired.
Ronald B. Morgan
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On Some Numerical Methods for Solving Large Differential Nonsymmetric Stein Matrix Equations
Mathematical and Computational Applications, 2022 In this paper, we propose a new numerical method based on the extended block Arnoldi algorithm for solving large-scale differential nonsymmetric Stein matrix equations with low-rank right-hand sides.
Lakhlifa Sadek +2 more
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Advanced Modeling and Simulation in Engineering Sciences, 2021 The main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties ...
Mohamed Abdelsabour Fahmy
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The power and Arnoldi methods in an algebra of circulants [PDF]
Numerical Linear Algebra with Applications, 2012 SUMMARYCirculant matrices play a central role in a recently proposed formulation of three‐way data computations. In this setting, a three‐way table corresponds to a matrix where each ‘scalar’ is a vector of parameters defining a circulant. This interpretation provides many generalizations of results from matrix or vector‐space algebra.
David F. Gleich +2 more
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