Computing eigenvalues of sparse matrices on the connection machine

  • V. A. Barker
  • Chen Yingqun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 879)


This paper discusses two Fortran subroutines, LANSYM and LANUSM, for computing eigenvalues of real sparse matrices on the CM-200. These subroutines are designed for symmetric and unsymmetric matrices, respectively. Both are adaptations of single-vector Lanczos algorithms developed by Cullum and Willoughby. The eigenvalues are computed in a region prescribed by the user. In the case of LANSYM, this is a real interval [a,b]. In the case of LANUSM, it is a quadrilateral, Q, in the complex plane. The main attractions of the Cullum and Willoughby approach are the absence of both the reorthogonalization of the Lanczos vectors and factorizations of the (shifted) input matrix.


Connection Machine eigenvalues Lanczos method sparse matrices 


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  1. CMSSL (1992). CMSSL Release Notes for the CM-200, Version 3.0, Thinking Machines Corporation, Cambridge, Mass.Google Scholar
  2. Cullum, J. K. and Willoughby, R. A. (1985a). Lanczos Algorithms tor Large Symmetric Eigenvalue Computations; Vol. 1, Theory. Birkhauser, Boston.Google Scholar
  3. Cullum, J. K. and Willoughby, R. A. (1985b). Lanczos Algorithms for Large Symmetric Eigenvalue Computations; Vol. 2, Codes. Birkhauser, Boston.Google Scholar
  4. Cullum, J. K. and Willoughby, R. A. (1986). A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices. In Large Scale Eigenvalue Problems, eds. J. K. Cullum and W. A. Willoughby, North-Holland, Amsterdam, pp. 193–240.Google Scholar
  5. Eispack (1976, 1977). Matrix Eigensystem Routines, eds. B. S. Garbow, J. M. Boyle, J. J. Dongarra and C. B. Moler. Lecture Notes in Mathematics, 6 and 51, Springer, New York.Google Scholar
  6. Paige, C. C. (1971). The computation of eigenvalues and eigenvectors of very large sparse matrices. Ph. D. Thesis, University of London.Google Scholar
  7. Paige, C. C. (1972). Computational variants of the Lanczos method for the eigenproblem. J. Inst. Math. Appl.,10, 373–381.Google Scholar
  8. Paige, C. C. (1976). Error analysis of the Lanczos algorithms for tridiagonalizing a symmetric matrix. J. Inst. Math. Appl.,18, 341–349.Google Scholar
  9. Paige, C. C. (1980). Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem. Linear Algebra Appl., 34, 235–258.Google Scholar
  10. Parlett, B. N. (1980). The Symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • V. A. Barker
    • 1
  • Chen Yingqun
    • 1
  1. 1.Institute of Mathematical Modelling, Numerical Analysis GroupTechnical University of DenmarkLyngbyDenmark

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