Results 171 to 180 of about 1,908 (194)
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Convergence of Arnoldi’s method for generalized eigenvalue problems
Afrika Matematika, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dookhitram, Kumar +2 more
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Implicitly Restarted Arnoldi Methods and Subspace Iteration
SIAM Journal on Matrix Analysis and Applications, 2001The paper is concerned with the relation of three methods for computing several eigenvalues of a matrix. 1. An implicitly restarted Arnoldi method. 2. Nonstationary simultaneous iteration (subspace iteration). 3. QR-algorithm. Numerical examples show that the first method can be much faster than the second one.
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Computing the Sobolev Regularity of Refinable Functions by the Arnoldi Method
SIAM Journal on Matrix Analysis and Applications, 2001Let a function \( \varphi \in L^2 ({\mathbb R}^d) \) be given by its refinement equation \[ \varphi (x) = |\det s |\sum_{j \in {\mathbb Z}^d} a(j) \varphi (sx-j), \qquad x \in {\mathbb R}^d , \] where \(s\) is a \(d \times d\) integer matrix with \( s^{\ast} s = \lambda I\) for some \( \lambda > 1\), and \(a = (a_j)_{j \in {\mathbb Z}^d} \) is a finite
Amos Ron, Zuowei Shen, Kim-Chuan Toh
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Krylov--Schur-Type Restarts for the Two-Sided Arnoldi Method
SIAM Journal on Matrix Analysis and Applications, 2017Summary: We consider the two-sided Arnoldi method and propose a two-sided Krylov-Schur-type restarting method. We discuss the restart for standard Rayleigh-Ritz extraction as well as harmonic Rayleigh--Ritz extraction. Additionally, we provide error bounds for Ritz values and Ritz vectors in the context of oblique projections and present ...
Ian N. Zwaan, Michiel E. Hochstenbach
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Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
SIAM Journal on Scientific Computing, 1998The authors are concerned with methods that are suited for the computation of a few eigenpairs of large, sparse eigenvalue problems of the form \(Ax=\lambda x\). They study an extension to the implicitly restarted Arnoldi technique for the generalized Davidson method which they call ``thick restarting''.
Andreas Stathopoulos +2 more
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A-posteriori residual bounds for Arnoldi’s methods for nonsymmetric eigenvalue problems
Numerical Algorithms, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kumar Dookhitram +3 more
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Improving eigenvectors in Arnoldi's method
2000The usual \(m\)-step Arnoldi method (searching for \(r\) eigenvalues and eigenvectors of a large unsymmetric matrix or operator \(A\) in the \(m\)-dimensional Krylov basis) does not usually make an explicit use of the (available) \((m+1)\)-st Krylov state.
Jia, ZX, Elsner, Ludwig
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Backward error analysis of an inexact Arnoldi method
PAMM, 2013AbstractWe investigate the behavior of Arnoldi's method for Hermitian matrices in the case of inexact vector operations. A special purpose variant of Gram Schmidt orthogonalization is introduced which computes a nearly orthogonal Krylov subspace basis and additionally implicitly provides an exactly orthogonal basis.
Ute Kandler, Christian Schröder
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An application of the Arnoldi's method to a geophysical fluid dynamics problem
Journal of Computational Physics, 1987A new method to find solutions of large linear systems, based on a projection on the Krylov subspace, is shown to be successful when applied to the linearized barotropic and baroclinic primitive equations. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be ...
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Multi-parameter Arnoldi-Tikhonov methods
2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
GAZZOLA, SILVIA, NOVATI, PAOLO
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