The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers
- Univ. of Kentucky, Lexington, KY (United States). Dept. of Mathematics
- Univ. of California, Berkeley, CA (United States)
- Univ. of Tennessee, Knoxville, TN (United States). Dept. of Computer Science
The implementation and performance of a class of divide-and-conquer algorithms for computing the spectral decomposition of nonsymmetric matrices on distributed memory parallel computers are studied in this paper. After presenting a general framework, the authors focus on a spectral divide-and-conquer (SDC) algorithm with newton iteration. Although the algorithm requires several times as many floating point operations as the best serial QR algorithm, it can be simply constructed from a small set of highly parallelizable matrix building blocks within Level 3 basic linear algebra subroutines (BLAS). Efficient implementations of these building blocks are available on a wide range of machines. In some ill-conditioned cases, the algorithm may lose numerical stability, but this can easily be detected and compensated for. The algorithm reached 31% efficiency with respect to the underlying PUMMA matrix multiplication and 82% efficiency with respect to the underlying ScaLAPACK matrix inversion on a 256 processor Intel Touchstone Delta system, and 41% efficiency with respect to the matrix multiplication in CMSSL on a 32 node Thinking Machines CM-5 with vector units. The performance model predicts the performance reasonably accurately. To take advantage of the geometric nature of SDC algorithms, they have designed a graphical user interface to let the user choose the spectral decomposition according to specified regions in the complex plane.
- Sponsoring Organization:
- Advanced Research Projects Agency, Washington, DC (United States); National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 532990
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 18, Issue 5; Other Information: PBD: Sep 1997
- Country of Publication:
- United States
- Language:
- English
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