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Monday, May 11, 2020 | History

4 edition of Preserving symmetry in preconditioned Krylov subspace methods found in the catalog.

Preserving symmetry in preconditioned Krylov subspace methods

Preserving symmetry in preconditioned Krylov subspace methods

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Published by Research Institute for Advanced Computer Science, NASA Ames Research Center, National Technical Information Service, distributor in [Moffett Field, Calif.], [Springfield, Va .
Written in English


Edition Notes

StatementTony F. Chan ... [et al.].
Series[NASA contractor report] -- NASA-CR-203271., RIACS technical report -- 96.19., NASA contractor report -- NASA CR-203271., RIACS technical report -- TR 96-19.
ContributionsChan, Tony F., Research Institute for Advanced Computer Science (U.S.)
The Physical Object
FormatMicroform
Pagination1 v.
ID Numbers
Open LibraryOL17593625M
OCLC/WorldCa40989499

conditioning and Krylov subspace iterations could provide efficient and simple “general- purpose” procedures that could compete with direct solvers. Preconditioning involves ex-File Size: 3MB. Similar Items. Preserving symmetry in preconditioned Krylov subspace methods Author(s): Chan, Tony F.; Chow, E.; Saad, Youcef ; Eigenvalue perturbation and the generalized Krylov subspace method.

EIGIFP.m: A matlab program that computes a few (algebraically) smallest or largest eigenvalues of a large symmetric matrix A or the generalized eigenvalue problem for a pencil (A, B). A x = lambda x or A x = lambda B x where A and B are symmetric and B is positive definite.. It is a black-box implementation of the inverse free preconditioned Krylov subspace method of. In the heart of Balanced Truncation methods, a sequence of projected generalized Lyapunov equations has to be solved. In this article we present a general framework for the numerical solution of projected generalized Lyapunov equations using preconditioned Krylov subspace methods based on iterates with a low-rank Cholesky factor by: 2.

where L, is another subspace of dimension m.A Krylov subspace method is a method for which the subspace I(, is the Krylov subspace in which TO = b - there is no ambiguity we will denote IKrylov subspace methods arise from different choices of the subspaces I(, and L, from the ways in which system is Size: 2MB.   In Sect. 4, we show that the resultant linear system has nonsymmetric Toeplitz matrices and design fast solution techniques based on preconditioned Krylov subspace methods to solve problem –. In Sect. 5, we present numerical experiments to show the effectiveness of the numerical method. Concluding remarks are given in Sect. : Huan-Yan Jian, Ting-Zhu Huang, Xi-Le Zhao, Yong-Liang Zhao.


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Preserving symmetry in preconditioned Krylov subspace methods Download PDF EPUB FB2

Preserving symmetry in preconditioned Krylov subspace methods (SuDoc NAS ) Unknown Binding – by NASA (Author)Author: NASA. We consider the problem of solving a linear system A x = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M.

In the symmetric case, we can Cited by: 6. Home Browse by Title Periodicals SIAM Journal on Scientific Computing Vol. 20, No. 2 Preserving Symmetry in Preconditioned Krylov Subspace Methods article Preserving Symmetry in Preconditioned Krylov Subspace Methods.

We consider the problem of solving a linear system A x = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M. In the symmetric case, we can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm.

This idea can also be used in the nonsymmetric case, and near symmetry can be preserved by: 6. Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.

1 Introduction Consider the solution of the linear system Ax = b (1) by a preconditioned Krylov subspace method. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M.

In the symmetric case, we can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm. Preserving symmetry in preconditioned Krylov subspace methods.

Authors: Chan, Tony F. Chow, E. Saad, Youcef Yeung, Man ChungCited by: 6. We believe the three iterative methods, BiCGSTAB, GMRES, and TFQMR, are most promising among the Krylov subspace methods and are representative.

Over the past years, efforts have been invested to compare various Krylov subspace methods, see, e.g., for some theoretical discussions, where no method was found to be the best for all problems by: Preconditioned Krylov subspace (KSP) methods are widely used for solving large‐scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs).

These linear systems are often nonsymmetric due to the nature of the PDEs, boundary or jump conditions, or discretization by: 3. Preserving Symmetry in Preconditioned Krylov Subspace Methods, T.

ChanI E. Chow} Y. Saadt and M. Yeungt November 6, Abstract We consider the problem of solving a linear system Ax = b when A is nearly sym- metric and when the system is preconditioned by a symmetric File Size: 1MB.

The inverse-free preconditioned Krylov subspace method of Golub and Ye [G.H. Golub, Q. Ye, An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems, SIAM J.

Sci. Comp. 24 () –] is an efficient algorithm for computing a few extreme eigenvalues of the symmetric generalized eigenvalue by: Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.

1 Introduction Consider the solution of the linear system Ax = b (1) by a preconditioned Krylov subspace : T. Chan, E. Chow, Y. Saad and M. Yeung. Preserving Symmetry in Preconditioned Krylov Subspace Methods eBook: National Aeronautics and Space Administration NASA: : Kindle StoreAuthor: National Aeronautics and Space Administration NASA.

Preserving symmetry in preconditioned Krylov subspace methods. By T. Chan, E. Chow, Y. Saad and M. Yeung. -inner products in the conjugate gradient (CG) algorithm.

This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the new algorithms are mathematically equivalent to split Author: T.

Chan, E. Chow, Y. Saad and M. Yeung. E-books. Browse e-books; Series Descriptions; Book Program; MARC Records; FAQ; Proceedings; For Authors. Journal Author Submissions; Book Author Submissions; Subscriptions.

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Journal / E Cited by: 2 Krylov subspace iterative methods 5 3 Symmetric and positive de nite matrices 8 but it is possible to precondition with Cwhilst preserving symmetry of the preconditioned system matrix; see Saad (, Algorithm ). (), or the recent book by M alek and Strako s ().

This can be a very valuable viewpoint. Indeed from this File Size: KB. Buy Preserving symmetry in preconditioned Krylov subspace methods (SuDoc NAS ) by NASA (ISBN:) from Amazon's Book Store. Everyday low prices and free delivery on eligible : NASA.

viii CONTENTS Convergence of GMRES Block Krylov Methods MINRES-QLP: A Krylov subspace method for indefinite or singular symmetric systems, SIAM J. Sci. Comput., published electronically Aug 4. To appear as Book Chapter. Preserving symmetry in preconditioned Krylov subspace methods.

Download: Preconditioned Krylov subspace methods for CFD applications. Download: [PDF] Preprint umsi, Minnesota Supercomputer Institute, Minneapolis, MNAugust. We first provide a brief review of the parallel preconditioned Krylov subspace methods in order to fix terminology and notations.

For details we refer to standard textbooks, e.g., [21, 40, 48].Request PDF | Absolute Diagonal Scaling Preconditioner of COCG Method for Symmetric Complex Matrix | The iterative method, i.e., Conjugate Orthogonal Conjugate Gradient (COCG) method .Get this from a library! Preserving symmetry in preconditioned Krylov subspace methods.

[Tony F Chan; Research Institute for Advanced Computer Science (U.S.);].