Comparisons of Parallel Preconditioners for the Computation of Interior Eigenvalues by the Minimization of Rayleigh Quotient


The KIPS Transactions:PartA, Vol. 10, No. 2, pp. 137-140, Jun. 2003
10.3745/KIPSTA.2003.10.2.137,   PDF Download:

Abstract

Recently, CG (Conjugate Gradient) scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for interior eigenvalues for the following eigenvalue problem, (Ax = λx) The given matrix A is assummed to be large and sparse, and symmetric. Also, the method is very amenable to parallel computations. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. We compare the parallel preconditioners for the computation of the interior eigenvalues of a symmetric matrix by CG-type method. The considered preconditioners are Point-SSOR, ILU (0) in the multi-coloring order, and Multi-Color Block SSOR (Symmetric Succesive OverRelaxation). We conducted our experiments on the CRAY-T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test matrices are up to 512x512 in dimensions and were created from the discretizations of the elliptic PDE. All things considered the MC-BSSOR seems to be most robust preconditioner.


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Cite this article
[IEEE Style]
S. B. Ma and H. J. Jang, "Comparisons of Parallel Preconditioners for the Computation of Interior Eigenvalues by the Minimization of Rayleigh Quotient," The KIPS Transactions:PartA, vol. 10, no. 2, pp. 137-140, 2003. DOI: 10.3745/KIPSTA.2003.10.2.137.

[ACM Style]
Sang Back Ma and Ho Jong Jang. 2003. Comparisons of Parallel Preconditioners for the Computation of Interior Eigenvalues by the Minimization of Rayleigh Quotient. The KIPS Transactions:PartA, 10, 2, (2003), 137-140. DOI: 10.3745/KIPSTA.2003.10.2.137.