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Balanced truncation model reduction of large-scale dense systems on parallel computers. (English) Zbl 0978.93013
The paper describes the design and use of parallel algorithms for model reduction of dense continuous-time stable LTI systems. First, three well-known balanced truncation (BF) algorithms requiring the computation of the Gramians are reviewed: the square-root (SR) algorithm, the balancing-free (BP) algorithm and the balancing-free square-root (BFSR) algorithm. The SR and the BFSR algorithms are selected for parallel implementation, where the Cholesky factors of the Gramians are replaced by full-rank factors. It results in a smaller arithmetic cost and workplace requirement for non-minimal systems. Then, a sign function-based solver for computing full-rank Cholesky factors is reviewed following the details given by P. Benner and E. S. Quintana-Ortí [Numer. Algorithms 20, 75-100 (1999; Zbl 0940.65035)]. The SVD of the product of the Cholesky factors with enhanced accuracy required in both above parallel algorithms is computed by using ScaLAPACK. Numerical experiments on a PC cluster evaluate the numerical accuracy and the parallel performance including the scalability of the above parallel algorithms comparing them with the analogous serial algorithms in SLICOT on two examples.

MSC:
93B11 System structure simplification
93B40 Computational methods in systems theory (MSC2010)
93A15 Large-scale systems
65Y05 Parallel numerical computation
Software:
LAPACK; ScaLAPACK; SLICOT
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