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    National Tsing Hua University Institutional Repository > 理學院 > 數學系 > 期刊論文 >  HOMOTOPY CONTINUATION METHOD FOR THE NUMERICAL-SOLUTIONS OF GENERALIZED SYMMETRICAL EIGENVALUE PROBLEMS


    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/45750


    Title: HOMOTOPY CONTINUATION METHOD FOR THE NUMERICAL-SOLUTIONS OF GENERALIZED SYMMETRICAL EIGENVALUE PROBLEMS
    Authors: DZENG DC;LIN WW
    教師: 林文偉
    Date: 1991
    Publisher: AUSTRALIAN MATHEMATICS PUBL ASSOC INC
    Relation: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS,Volume: 32,Pages: 437-456,Part: Part 4,Published: APR 1991
    Keywords: ALGORITHM
    Abstract: We consider a generalised symmetric eigenvalue problem Ax = lambda-Mx, where A and M are real n by n symmetric matrices such that M is positive semidefinite. The purpose of this paper is to develop an algorithm based on the homotopy methods in [9, 11] to compute all eigenpairs, or a specified number of eigenvalues, in any part of the spectrum of the eigenvalue problem Ax = lambda-Mx. We obtain a special Kronecker structure of the pencil A-lambda-M, and give an algorithm to compute the number of eigenvalues in a prescribed interval. With this information, we can locate the lost eigenpair by using the homotopy algorithm when multiple arrivals occur. The homotopy maintains the structures of the matrices A and M (if any), and the homotopy curves are n disjoint smooth curves. This method can be used to find all/some isolated eigenpairs for large sparse A and M on SIMD machines
    URI: http://jupiter.math.nctu.edu.tw/~wwlin/papers_new/1991DLp.pdf
    http://www.austms.org.au/
    http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/45750
    Appears in Collections:[數學系] 期刊論文

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