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Complexity of Kronecker Operations on Sparse Matrices with Applications to the Solution of Markov Models (1997)

Buchholz, Peter ; Donatelli, Susanna ; Kemper, Peter ; [et al.]

In: CASI

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Publication Date: 2019-06-28

Description: We present a systematic discussion of algorithms to multiply a vector by a matrix expressed as the Kronecker product of sparse matrices, extending previous work in a unified notational framework. Then, we use our results to define new algorithms for the solution of large structured Markov models. In addition to a comprehensive overview of existing approaches, we give new results with respect to: (1) managing certain types of state-dependent behavior without incurring extra cost; (2) supporting both Jacobi-style and Gauss-Seidel-style methods by appropriate multiplication algorithms; (3) speeding up algorithms that consider probability vectors of size equal to the "actual" state space instead of the "potential" state space.

Keywords: Computer Programming and Software

Type: NASA/CR-97-206274 , NAS 1.26:206274 , ICASE-97-66

Format: application/pdf

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