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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.

93B11 System structure simplification
93B40 Computational methods in systems theory (MSC2010)
93A15 Large-scale systems
65Y05 Parallel numerical computation
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