3 edition of **Using parallel banded linear system solvers in generalized Eigenvalue problems** found in the catalog.

Using parallel banded linear system solvers in generalized Eigenvalue problems

Zhang, Hong.

- 40 Want to read
- 4 Currently reading

Published
**1993**
by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va
.

Written in English

- Eigenvalues.

**Edition Notes**

Statement | Hong Zhang, William F. Moss. |

Series | NASA contractor report -- 191540., ICASE report -- no. 93-71., NASA contractor report -- NASA CR-191540., ICASE report -- no. 93-71. |

Contributions | Moss, William F., Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL14702879M |

In addition, Julia provides many factorizations which can be used to speed up problems such as linear solve or matrix exponentiation by pre-factorizing a matrix into a form more amenable (for performance or memory reasons) to the problem. Vector and Parallel Processing – VECPAR’98 Third International Conference, Porto, Portugal, June , Eigenvalue Problems and Solution of Linear Systems. Parallel Jacobi-Davidson for Solving Generalized Eigenvalue Problems. Margreet Nool, Auke van der Ploeg.

Freely Available Software for Linear Algebra on the Web. Tables present a list of freely available software for the solution of linear algebra problems. The interest is in software for high-performance computers that is available in "open source" form on the web for solving problems in numerical linear algebra, specifically dense, sparse direct and iterative systems . If a linear transformation acts on a vector and the result is only a change in the vector's magnitude, not direction, that vector is called an eigenvector of that particular linear transformation, and the magnitude that the vector is changed by is .

Using parallel banded linear system solvers in generalized eigenvalue problems Journal Article Zhang, H ; Moss, W F - Parallel Computing Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c.

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A parallel algorithm for the banded generalized eigenvalue problem In this section, we consider generalized symmetric eigenproblems of the form Ax=ABx, (3) where A and B are symmetric, m-banded matrices and B is positive definite. We wish to approximate the q, q eigenvalues A1 Cited by: Get this from a library.

Using parallel banded linear system solvers in generalized Eigenvalue problems. [Hong Zhang; William F Moss; Langley Research Center.]. Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems.

This paper discusses an algorithm that makes use of two parallel banded solvers Author: Hong Zhang and William F. Moss. Using parallel banded linear system solvers in generalized eigenvalue problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration.

A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an Author: William F.

Moss and Hong Zhang. Efficient parallel implementation of eigenvalue solvers for banded generalized Hermitian eigenvalue problems. • Parallel reduction of the generalized banded symmetric eigenproblem to a standard eigenproblem. • Scalable parallel algorithm.

• Efficient transformation especially for thin banded : Michael Rippl, Bruno Lang, Thomas Huckle. The Stable Parallel Solution of General Narrow Banded Linear Systems interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing.

() Using parallel banded linear system solvers in generalized eigenvalue problems. Parallel Computing() A Parallel Algorithm for Computing the Singular Value Decomposition of a by: In this paper we consider solution of the eigen problem in structural analysis using a recent version of the Lanczos method and the subspace method.

The two methods are applied to examples and we conclude that the Lanczos method. The parallel homotopy algorithm for finding few or all eigenvalues of a symmetric tridiagonal matrix is presented.

The computations were executed on an NCUBE, a distributed memory multiprocessor. T Cited by: Solve the dense linear system Ax = b using the approximate block LU Factorization algorithm with the procedure of ”diagonal boosting” Let α be a multiple of the unit roundoff, e.g.

10−6, and aj be the jth column of the updated matrix A after step j − 1. By using recently developed solvers for linear systems of equations and for generalized eigenvalue problems, results for reasonable spatial resolution can be obtained.

4 The FEAST Eigensolver Interior eigenvalue problems Compute eigenvalue by solving linear systems Standard/generalized Hermitian/non-Hermitian problems Matrix format independent – Banded, sparse and dense predefined interfaces – Can import a custom linear solver through RCI J.

Kestyn, E. Polizzi, P.T.P Tang, SIAM Journal on Scientific Computing (SISC), 38, S. Abstract. In this paper we present a parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem A x = λB x, where A and B are large sparse matrices. A moment-based method by which to find all of the eigenvalues that lie inside a given domain is by: 6.

taining directly the eigenpairs solutions using the density matrix representation and a numerically eﬃcient contour integration technique.

III. FEAST A. Introduction In this section, a new algorithm is presented for solving generalized eigenvalue problems of this form Ax = λBx, (2) within a given interval [λ min,λ max], where A is real sym-File Size: KB. To solve such problems, we develop parallel preconditioned solvers to find a few eigenvalues and-vectors from one end of the spectrum based on the Jacobi-Davidson (JD) method by G.L.G.

Sleijpen and H.A. van der Vorst [5]. For preconditioning, we apply banded matrices and a new adaptive approach using the QMR iteration. The exact ﬁrst eigenvalue of this problem is λ1 = π2d 4. The background of this problem is the Electronic Schrodinger Equation in Rd, see [5]. N is the approximate function space satisfying the corresponding boundary conditions.

k is is the Legendre polynomial of degree. Amherst Brendan Gavin Non-linear eigenvector problem Team expanded subspace scheme Braegan Spring SPIKE-SMP v v scalable banded system solver FEAST banded interfaces upgrade Peter Tang General FEAST algorithm analysis Intel improved schemes Collaborators Yousef Saad Eigenvalue count estimates & U.

of Minnesota new FEAST Cited by: 2. This section describes the LAPACK routines for solving systems of linear equations. Before calling most of these routines, you need to factorize the matrix of your system of equations (see Routines for Matrix Factorization).

However, the factorization is not necessary if your system of equations has a triangular matrix. This paper presents two parallel banded linear solvers and their application for general- ized positive definite eigenvalue problems, in which, only a few of the smallest eigenvalues and corresponding eigenvectors are needed to moderate accuracy.

This type of problem arisesCited by: jI A) were banded with semi-bandwidthhaving in average 12 nonzero entries per row. Thus, the linear systems (z jI A)V = Y were solved using a parallel banded solver.

The results are shown in Table 1. As it can be seen, we sought eigenpairs with eigenvalue around zero. The residuals were required to be below tol = 10 8, in fact most of the.

Mark T. Jones has written: 'Bunch-Kaufman factorization for real symmetric indefinite banded matrices' -- subject(s): Bunch-Kaufman algorithm, Matrices 'The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem' -- subject(s): Algorithms, Buckling, Problem solving.The following methods provide the solution of the linear system of equations Ku = P.

Each solver is tailored to a specific matrix topology. Profile SPD -- Direct profile solver for symmetric positive definite matrices; Band General -- Direct solver for banded unsymmetric matrices; Band SPD -- Direct solver for banded symmetric positive definite.banded symmetric generalized eigenproblems, especially in the case of large scale problems.

This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations.