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Thursday, May 7, 2020 | History

2 edition of A parallel algorithm for symmetric tridiagonal eigenvalue problems found in the catalog.

A parallel algorithm for symmetric tridiagonal eigenvalue problems

by Hui-ming Huang

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Published by Center for Advanced Computation, University of Illinois at Urbana - Champaign in Urbana, Ill .
Written in English

    Subjects:
  • Eigenvalues,
  • Algorithms

  • Edition Notes

    Statementby Hui-ming Huang
    SeriesCAC document -- no. 109, CAC document -- no. 109.
    ContributionsUniversity of Illinois at Urbana-Champaign. Center for Advanced Computation
    The Physical Object
    Paginationiv, 53 leaves :
    Number of Pages53
    ID Numbers
    Open LibraryOL25334102M
    OCLC/WorldCa793916239

    Li TY, Zou XL. Implementing the parallel quasi-Laguerre's algorithm for symmetric tridiagonal eigenproblems SIAM J SCI COMPUT (6) JUL 22 ; Tisseur F, Dongarra J. A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures SIAM J SCI COMPUT (6) JUL 22 Preconditioned Jacobi SVD Algorithm Outperforms PDGESVD. Parallel Processing and Applied Mathematics, () A harmonic FEAST algorithm for non-Hermitian generalized eigenvalue problems. Linear Algebra and its Applications , Divide and Conquer Symmetric Tridiagonal Eigensolver for Multicore by:

    efficiently, which leads to a new stable algorithm for solving symmetric tridiagonal eigenvalue problems. It is about as accurate as other well-known algorithms, and it is faster than one might expect. Although it is not the fastest algorithm available, it is comparable in File Size: KB. The workload in the QL algorithm is O(n3) per iteration for a general matrix, which is prohibitive. However, the workload is only O(n) per iteration for a tridiagonal matrix and O(n2) for a Hessenberg matrix, which makes it highly efficient on these forms. In this section we are concernedonlywith the case whereA is a real, symmetric File Size: 84KB.

    the eigenvalue problem (), and a corresponding solution x x(i) of () eigensolution belonging to the eigenvalue i. The following chapters provide the main theoretical results and algorithms on the eigenvalue problem for symmetric matrix. Chapter 2 introduces the basic facts on eigenvalues. Chapter 3 introduces Toeplitz Systems. ChapterFile Size: KB. A Parallel Algorithm for Solving General Tridiagonal Equations By Paul N. Swarztrauber* Abstract. A parallel algorithm for the solution of the general tridiagonal system is presented. The method is based on an efficient implementation of Cramer's rule, in which the .


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A parallel algorithm for symmetric tridiagonal eigenvalue problems by Hui-ming Huang Download PDF EPUB FB2

In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix.

We extend this idea to obtain a parallel algorithm that retains a number of active parallel processes that is greater than or equal to the initial number Cited by: An efficient parallel algorithm, which we dubbed farm- zeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with In this article, a fully scalable parallel algorithm is presented for solving symmetric tridiagonal eigenvalue problems using quasi-Laguerre's method.

The algorithm is implemented using PVM and tested on a variety of matrices with a load balancing scheme. Test results show Cited by: 1. Abstract. In this paper we present an algorithm, parallel in nature, for finding eigenvalues of a symmetric definite tridiagonal matrix pencil.

Our algorithm employs the determinant evaluation, split-and-merge strategy and Laguerre's by: 6. A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem Conference Paper (PDF Available) in SIAM Journal on Scientific and Statistical Computing 8(2) January with Reads.

In Matrix Computations by Golub and Van Loan (3rd edition, page ) an algorithm is given for a parallel version of the classical Jacobi algorithm for solving a real symmetric eigenvalue problem.

This question is related to my previous question The algorithm to find the largest eigenvalue and one of its eigenvector of a symmetric tridiagonal matrix. The matrix in question is a symmetric Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn.

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: Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation (−) =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.

When k = 1, the vector is called simply an eigenvector, and the pair. Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR basic concept behind these algorithms is the divide-and-conquer approach from computer science.

The q -I- I symmetric positive definite systems (14) may be solved simultaneously by q -I- I (or less) different processors. Parallel algorithm 19 3. NUMERICAL EXPERIMENTS The choice of the method for solving the systems (9) (or (14)) depends on the structure and Cited by: which are amenable to various parallel architectures.

The divide and conquer method is the fastest now avail-able if all eigenvalues and eigenvectors of a symmetric tridiagonal matrix are desired. The method, implemented in LAPACK [12], begins with dividing the original matrix into two smaller symmetric tridiagonal matrices, computing the.

A New O(n2) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem by Inderjit Singh Dhillon Doctor of Philosophy in Computer Science University of California, Berkeley Professor James W.

Demmel, Chair Computing the eigenvalues and orthogonal eigenvectors of an n ×n symmetric tridiagonal. For the ADC2 algorithm, a method is proposed to estimate the off-diagonal rank. Numerous experiments have been done to show their stability and efficiency.

These algorithms are implemented in parallel in a shared memory environment, and. The user manual includes references to several different methods for solving eigenvalue problems.

share | cite | improve this answerA parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures, for the parallel tridiagonal eigensolve.

It can compute all of the eigenpairs of the. Serial computation combined with high communication costs on distributed-memory multiprocessors make parallel implementations of the QR method for the nonsymmetric eigenvalue problem inefficient.

This paper introduces an alternative algorithm for the nonsymmetric tridiagonal eigenvalue problem based on rank two tearing and updating of the matrix. In this paper, we propose a parallel iterative method for calculating the extreme eigenpair (the largest or smallest eigenvalue and corresponding eigenvector) of a large symmetric tridiagonal matrix.

It is based upon a divide and repeated, rank-one modification : Zhenyue Zhang. eigenvalues in the sequential case. A parallel algorithm for multicomputers that uses this method can be found in [27]. In the symmetric tridiagonal case the cost of the QR factorization is of O(n).

However, there are not efficient scalable parallel implementations of this method, so other approaches are being considered for parallel architectures. An O(log2N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix by Paul N.

Swarz_rauber 1,2 December ABSTRACT An O(loglN) parallel algorithm is presented for computing the eigenvalues of a symmetric tridlagonal matrix using a parallel algorithm for computing the zeros of the characteristic Size: KB.

parallel algorithm developed in [ 17, 19] for computing the characteristic polyno-mial. Krishnakumar and Morf [10] also use this parallel algorithm to compute the eigenvalues of a symmetric tridiagonal matrix in O(NXogN) time; how-ever, their method of separating the zeros is different from the one presented here.

In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.A tridiagonal system for n unknowns may be written as − + + + =, where = and.

[⋱ ⋱ ⋱ −] [⋮] = [⋮].For such systems, the solution can be obtained.parallel computers. Key–Words: Symmetric tridiagonal eigenvalue problem, heterogeneous parallel computing, load balancing 1 Introduction Computation of the eigenvalues of a symmetric tridi-agonal matrix is a problem of great relevance in nu-merical linear algebra and in many engineering fields, mainly due to two reasons: first, this kind of.Bini D and Pan V Parallel complexity of tridiagonal symmetric Eigenvalue problem Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms, () Gallopoulos E and Saad Y On the parallel solution of parabolic equations Proceedings of the 3rd international conference on Supercomputing, ().