A Parallel Method for the Computation of Matrix Exponential Based on Truncated Neumann Series

This paper introduces a new method for computing matrix exponential based on truncated Neumann series. The efficiency of the method is based on smart factorizations for evaluation of several Neumann series that can be done in parallel and divided across different processors with low communication ov...

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Bibliographic Details
Main Authors: Dimitrov, Vassil, Ariyarathna, Viduneth, Coelho, Diego F. G., Rakai, Logan, Madanayake, Arjuna, Cintra, Renato J.
Format: Conference Proceeding
Language:English
Subjects:
Approximation algorithms
Eigenvalues and eigenfunctions
Error analysis
Fast algorithms
Hardware
Matrix exponential
Neumann series
Program processors
Software algorithms
VLSI
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Summary:This paper introduces a new method for computing matrix exponential based on truncated Neumann series. The efficiency of the method is based on smart factorizations for evaluation of several Neumann series that can be done in parallel and divided across different processors with low communication overhead. A physical realization on FPGA is provided for proof-of-concept. The method is verified to be advantageous over the usual Horner's rule approach for polynomial evaluation. The hardware verification shows a reduction of 62% in time required for processing for series approximations with 9 terms. Software verification demonstrates a 30% reduction in time compared to Horner's rule and the trade-offs between using a higher precision approach is illustrated.
ISSN:1063-6889
DOI:10.1109/ARITH.2017.23