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1.
Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant
subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the
family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's
equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted
in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is
close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments
are reported.
Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001 相似文献
2.
Miloud Mihoubi 《Discrete Mathematics》2008,308(12):2450-2459
This paper concerns the study of the Bell polynomials and the binomial type sequences. We mainly establish some relations tied to these important concepts. Furthermore, these obtained results are exploited to deduce some interesting relations concerning the Bell polynomials which enable us to obtain some new identities for the Bell polynomials. Our results are illustrated by some comprehensive examples. 相似文献
3.
A fast algorithm for solving systems of linear equations with banded Toeplitz matrices is studied. An important step in the algorithm is a novel method for the spectral factorization of the generating function associated with the Toeplitz matrix. The spectral factorization is extracted from the right deflating subspaces corresponding to the eigenvalues inside and outside the open unit disk of a companion matrix pencil constructed from the coefficients of the generating function. The factorization is followed by the Woodbury inversion formula and solution of several banded triangular systems. Stability of the algorithm is discussed and its performance is demonstrated by numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
4.
A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices 总被引:1,自引:0,他引:1
Miloud Sadkane 《Numerische Mathematik》1993,64(1):181-193
Summary In this paper we describe a block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts. The method is accelerated via Chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum. A parallel implementation of this method is investigated on the eight processor Alliant FX/80. Numerical results and comparisons with simultaneous iteration on some Harwell-Boeing matrices are reported. 相似文献
5.
This paper develops algebraic and convergence properties of the left and right block reflectors used in the block diagonalization algorithm. Several numerical illustrations are reported.AMS subject classification (2000) 65F20, 15A23.Submitted December 2002. Accepted October 2003. Communicated by Per Christian Hansen. 相似文献
6.
Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems 总被引:3,自引:0,他引:3
The Davidson method is a preconditioned eigenvalue technique aimed at computing a few of the extreme (i.e., leftmost or rightmost)
eigenpairs of large sparse symmetric matrices. This paper describes a software package which implements a deflated and variable-block
version of the Davidson method. Information on how to use the software is provided. Guidelines for its upgrading or for its
incorporation into existing packages are also included. Various experiments are performed on an SGI Power Challenge and comparisons
with ARPACK are reported.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
This paper presents an algorithm for the numerical approximation of spectral projectors onto the invariant subspaces corresponding
to the eigenvalues inside, on, and outside the unit circle of a symplectic matrix. The algorithm constructs iteratively three
matrix sequences from which the projectors are obtained. The convergence depends essentially on the gap between the unit circle
and the eigenvalues inside it. A larger gap leads to faster convergence. Theoretical and algorithmic aspects of the algorithm
are developed. Numerical results are reported. 相似文献
8.
The behavior of ChebFilterCG (an algorithm that combines the Chebyshev filter and Conjugate Gradient) applied to systems with unfavorable eigenvalue distribution is examined. To improve the convergence, a hybrid approach combining a stabilized version of the block conjugated gradient with Chebyshev polynomials as preconditioners (ChebStaBlkCG) is proposed. The performance of ChebStaBlkCG is illustrated and validated on a set of linear systems. It is shown how ChebStaBlkCG can be used to accelerate the block Cimmino method and to solve linear systems with multiple right‐hand sides. 相似文献
9.
10.
Peter Benner Grece El Khoury Miloud Sadkane 《Numerical Linear Algebra with Applications》2014,21(5):645-665
A squared Smith type algorithm for solving large‐scale discrete‐time Stein equations is developed. The algorithm uses restarted Krylov spaces to compute approximations of the squared Smith iterations in low‐rank factored form. Fast convergence results when very few iterations of the alternating direction implicit method are applied to the Stein equation beforehand. The convergence of the algorithm is discussed and its performance is demonstrated by several test examples. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献