Solving Eigenproblems on Multicomputers: Two Different Approaches

E.M. Garzón and I. García

References

  1. [1] J.K. Cullum & R.A. Willoughby, Lanczos algorithms for largesymmetric eigenvalue computations, Vol. 1: Theory; Vol. 2:Programs (Stuttgart: Birkhäuser, 1985).
  2. [2] A. Basermann & P. Weidner, A parallel algorithm for determining all eigenvalues of large real symmetric tridiagonal matrices, Parallel Computing, 18(10), 1992, 1129–1141. doi:10.1016/0167-8191(92)90060-K
  3. [3] G.H. Golub & C.F. Van Loan, Matrix computations, 3rd ed.(Baltimore: Johns Hopkins University Press, 1996).
  4. [4] J.J.M. Cuppen, A divide and conquer method for the symmetriceigenproblem, Numerische Mathematik, 2(36), 1981, 177–195. doi:10.1007/BF01396757
  5. [5] E.M. Garzón & I. García, Evaluation of the work load balancein irregular problems using value based data distributions, Proc.IASTED Euro-PDS’97, Barcelona, 1997, 137–143.
  6. [6] I.C.F. Ipsen & E.R. Jessup, Solving the symmetric tridiagonal eigenvalue problem on the hypercube, SIAM Journal onScientific and Statistical Computing, 11(2), 1990, 203–229. doi:10.1137/0911013
  7. [7] M.W. Berry, Large-scale sparse singular value computations,International Journal of Supercomputer Applications, 6(1),1992, 13–49.
  8. [8] H.D. Simon, Analysis of the symmetric Lanczos algorithmwith reorthogonalization methods, Linear Algebra and ItsApplications, 61, 1984, 101–131. doi:10.1016/0024-3795(84)90025-9
  9. [9] H.J. Bernstein, An accelerated bisection method for the calculation of eigenvalues of a symmetric tridiagonal matrix, Numerische Mathematik, 43(1), 1984, 153–160. doi:10.1007/BF01389644
  10. [10] J.H. Wilkinson, The algebraic eigenvalue problem (Oxford:Oxford University Press, 1965; reprinted 1988).
  11. [11] G.H. Golub, Some modified matrix eigenvalue problems, SIAMReview, 15(2), 1973, 318–344. doi:10.1137/1015032
  12. [12] J.R. Bunch, C.P. Nielsen, & D.C. Sorensen, Rank one modification of the symmetric eigenproblem, Numerische Mathematik, 31(1), 1978, 31–48. doi:10.1007/BF01396012
  13. [13] E.M. Garzón & I. García, Parallel implementation of theLanczos method for sparse matrices: Analysis of data distributions, Proc. Int. Conf. on Supercomputing (New York: ACM Press, 1996), 294–300. doi:10.1145/237578.237622
  14. [14] J.J. Dongarra & D.C. Sorensen, A fully parallel algorithm forthe symmetric eigenvalue problem, SIAM Journal on Scientificand Statistical Computing, 8(2), 1987, 139–154. doi:10.1137/0908018
  15. [15] F. Tisseur & J. Dongarra, A parallel divide and conqueralgorithm for the symmetric eigenvalue problem on distributedmemory architectures, SIAM Journal on Scientific Computing,20(6), 1999, 2223–2236. doi:10.1137/S1064827598336951
  16. [16] I.S. Duff, R.G. Grimes, & J.G. Lewis, Sparse matrix test problems, ACM Trans. on Mathematical Problems, 15(1), 1989, 1–14. doi:10.1145/62038.62043
  17. [17] U. Nagashima, S. Hyugaji, S. Sekiguchi, M. Sato, & H. Hosoya,An experience with super-linear speedup achieved by parallelcomputing on a workstation cluster: Parallel calculation ofdensity of states of large scale cyclic polyacenes, ParallelComputing, 21, 1995, 1491–1504. doi:10.1016/0167-8191(95)00026-K
  18. [18] B. Vasiliu & S.C. Kothari, Parallelization of waveguide program and performance on a cluster of PCs, http://www.cs.iastate.edu/kothari/
  19. [19] J.L. Gustafson, Reevaluating Amdahl’s Law, Comm. ACM,1988, 532–533. doi:10.1145/42411.42415
  20. [20] E.M. Garzón & I. García, A parallel implementation of theeigenproblem for large, symmetric and sparse matrices, RecentAdvances in PVM and MPI, LNCS 1697 (Heidelberg, Germany:Springer-Verlag, 1999), 380–387.
  21. [21] E.M. Garzón & I. García, Parallel implementation for large and sparse eigenproblems, Acta Cybernetica, 15, 2001, 137-149

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