Parallel Partial Stabilizing Algorithms for Large Linear Control Systems
The Journal of Supercomputing
Parallel algorithms for LQ optimal control of discrete-time periodic linear systems
Journal of Parallel and Distributed Computing
Fast solution of large N × N matrix equations in an MIMD-SIMD hybrid system
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
State-space truncation methods for parallel model reduction of large-scale systems
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
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Optimization Methods & Software
Principal component analysis for distributed data sets with updating
APPT'05 Proceedings of the 6th international conference on Advanced Parallel Processing Technologies
Parallel model reduction of large linear descriptor systems via balanced truncation
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
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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, we 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. Our performance model predicts the performance reasonably accurately.To take advantage of the geometric nature of SDC algorithms, we have designed a graphical user interface to let the user choose the spectral decomposition according to specified regions in the complex plane.