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Tuesday, July 28, 2020 | History

5 edition of Parallel computation of eigenvalues of real matrices found in the catalog.

Parallel computation of eigenvalues of real matrices

by David J. Kuck

  • 320 Want to read
  • 34 Currently reading

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

    Subjects:
  • Matrices -- Data processing.,
  • Eigenvalues -- Data processing.,
  • Parallel processing (Electronic computers),
  • Illiac computer -- Programming.

  • Edition Notes

    Statementby David J. Kuck [and] Ahmed Sameh.
    Series[Illinois. University at Urbana-Champaign. Center for Advanced Computation] CAC document no. 9
    ContributionsSameh, Ahmed, joint author.
    Classifications
    LC ClassificationsQA76 .I4 no.487, QA188 .I4 no.487
    The Physical Object
    Pagination39 p.
    Number of Pages39
    ID Numbers
    Open LibraryOL5393022M
    LC Control Number72610344

    () A matrix-less and parallel interpolation–extrapolation algorithm for computing the eigenvalues of preconditioned banded symmetric Toeplitz matrices. Numerical Algorithms , () Exact Variance Ratio Test with Overlapping by: Methods for Computing Eigenvalues and Eigenvectors 10 De nition The characteristic polynomial of A, denoted P A (x) for x 2 R, is the degree n polynomial de ned by P A (x) = det(xI A): It is straightforward to see that the roots of the characteristic polynomial of a matrix .

    Eigensystem finds numerical eigenvalues and eigenvectors if m contains approximate real or complex numbers.; For approximate numerical matrices m, the eigenvectors are normalized.; For exact or symbolic matrices m, the eigenvectors are not normalized.; All the nonzero eigenvectors given are independent. If the number of eigenvectors is equal to the number of nonzero eigenvalues. It doesn't make much sense to compute the eigenvalues without their multiplicity and then say "since the eigenvalues are real, the matrix is diagonalizable" because it doesn't hold in general. It does hold for symmetric matrices but symmetric matrices have real eigenvalues and are diagonalizable so there is no need to calculate anything to.

    An O(log²N) parallel algorithm for computing the Eigenvalues of a symmetric tridiagonal matrix [microform] / Paul N. Swarztrauber Research Institute for Advanced Computer Science, NASA Ames Research Center ; For sale by the National Technical Information Service [Moffett Field, Calif.?]: [Springfield, Va Australian/Harvard Citation. Properties. A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal. Although a general tridiagonal matrix is not necessarily symmetric or Hermitian, many of those that arise when solving linear algebra problems have .


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Parallel computation of eigenvalues of real matrices by David J. Kuck Download PDF EPUB FB2

DvancedComputation TURBANA-CHAMPAIGN OIS CACDocumentNo.9 DCSReportNo.I+87 PARALLELCOMPUTATIONOF EIGENVALUESOFREALMATRICES BY AhmedSameh November1, Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.

Parallel computation of eigenvalues of real matrices in SearchWorks catalog Skip to search Skip to main content.

Parallel Computation of Eigenvalues of Real Matrices. Conference Paper (PDF Available)   January   with  14 Reads  How we measure 'reads' A. Enter the password to open this PDF file: Cancel OK. File name:. Weston J., Szularz M., Clint M., Murphy K. () The parallel computation of partial eigensolutions of large matrices on a massively parallel processor.

In: Bougé L., Fraigniaud P., Mignotte A., Robert Y. (eds) Euro-Par'96 Parallel Processing. Euro-Par Lecture Notes in Computer Science, vol Cited by: 1. A parallel implementation of an algorithm to compute the eigenvalues of a real symmetric matrix using a MIMD machine is described.

An array of Transputers configured in a ring topology is used as a processor farm for the computation. The speedup obtained by using P processors asymptotically approaches P when the size of (he problem becomes : L.

Waring, M. Clint. The parallel calculation of the eigenvalues of a real matrix A Aj,Ai, = 2 (-re-i -Zi,FZa-u)AZu + Z.-i.R-i [ (Zu "F Z,-in-i)2 - 4 (ZijZn-i.n-- Zi.n-iZn-lj)]`~.

() 5. AVOIDANCE OF BREAKDOWN BY COLUMN INTERCHANGES In the previous section, it was assumed that every matrix of the sequence A; could be factorized into the product WZ.Cited by: 5. A concurrent algorithm for parallel calculation of eigenvalues and eigenvectors of real symmetric matrices Article in Journal of Computational Chemistry 13(2) - September with 6 Reads.

I don't need all the eigenvalues, just some largest or smallest eigenvalues. I have a similarity matrix of image, so this matrix is very large. So I think parallelism for the computation will get better performance. But I'm new in parallel computation. So I really need some guides. Thanks.

$\endgroup$ – HongTu Apr 26 '12 at The parallel analysis for this example indicates that two components should be retained. There are two ways to tell this; (1) two of the eigenvalues in the PCA column are greater than the average eigenvalues in the PA column, and (2) the dashed line for parallel analysis in the graph crosses the solid pca line before reaching the third component.

Introduction. The computation of the eigenvalues of a symmetric Toeplitz matrix is a task that appears quite often in digital signal processing and control applications.

The eigenvalue problem for symmetric real matrices can be stated as: (1) A x = λ x, where A ∈ R n × n, x ≠ 0 ∈ C n, λ ∈ algorithms to be applied to solve this problem depend mainly on the concrete Cited by: 7. matrices, both general [20], [21], [46] and banded [13].

In the same way some numerical methods to obtain the eigenvalues and eigenvectors of symmetric Toeplitz matrices generated by rational functions [43], or to obtain its generalised eigenvalues and eigenvectors [14]. Erricos John: Handbook on Parallel Computing and Statistics DK c /7/20 Parallel Algorithms for the Singular Value Decomposition has eigenvalues σ1 2 ≥≥σn 2 ≥ 0, corresponding to the eigenvectors (vi), (i = 1,n).

The symmetric matrix. () A matrix-less and parallel interpolation–extrapolation algorithm for computing the eigenvalues of preconditioned banded symmetric Toeplitz matrices. Numerical Algorithms () Asymptotics of eigenvalues and eigenvectors of Toeplitz by: ().

THE QZ ALGORITHM FOR THE CALCULATION OF THE EIGENVALUES OF A REAL MATRIX. Parallel Algorithms and Applications: Vol. 4, No.pp. Key words. parallel computing, symmetric matrix, eigenvalues, eigenvectors, relatively robust representations AMS subject classifications.

65F15, 65Y05, 68W10 DOI. / 1. Introduction. The symmetric eigenvalue problem is ubiquitous in computa-tional sciences; problems of ever-growing size arise in applications as varied as com. The main contribution of this paper is to present an efficient GPU implementation of bulk computation of eigenvalues for many small, non-symmetric, real matrices.

This work is motivated by the necessity of such bulk computation in designing of control systems, which requires to compute the eigenvalues of hundreds of thousands non-symmetric real Cited by: 4.

Exercise 6 Show by direct computation that the matrices A and B of Ex-ample 2 have the same characteristic equation. What are the eigenvalues of A and B. 2 Diagonalizable Matrices Definition 7 A diagonal matrix is a square matrix with all of its o ff—diagonal entries equal to zero.

Example 8 The matrix B = 0 −50 is a diagonal Size: KB. Typically, people take a real-valued matrix and view it as a complex-valued matrix for the purpose of finding eigenvalues, since then the field of scalars is algebraically closed.

But the definition of an eigenvalue is geometric, after all, so if a matrix has no eigenvectors in our space it cannot have any eigenvalues either. $\endgroup. A trivial suggestion: try your code on smaller matrices, first.

Your first example is correct but makes no or little sense on your machine. By default matlab will use multithreaded routines on multi core cpus; using smpd on 2 workers, one for each core, you will experience a slowdown with respect to the multithread (default) computation.

Your second example will perform the same computation. A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra.

It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text.

This third edition corrects several errors in the text and updates the font faces.4/5(1).The first numerical algorithm for computing eigenvalues and eigenvectors appeared inwhen Richard von Mises published the power method.

One of the most popular methods today, the QR algorithm, was proposed independently by John G. F. Francis and Vera Kublanovskaya in Eigenvalues and eigenvectors of matrices.Find the Eigen Values for Matrix. The first step into solving for eigenvalues, is adding in a along the main diagonal. Now the next step to take the determinant.

Now lets FOIL, and solve for. Now lets use the quadratic equation to solve for. In this problem, we will get three eigen values and eigen vectors since it's a symmetric matrix.