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Optimizing the Computation of Eigenvalues Using Graphics Processing Units

Ion Lungu, Alexandru Pirjan, Dana-Mihaela Petrosanu
Economic Informatics Department, Academy of Economic Studies, Bucharest, Romania
Universitatea Politehnica Bucuresti Scientific Bulletin, Series A, Vol. 74, Iss. 3, 2012

@article{lungu2012optimizing,

   title={OPTIMIZING THE COMPUTATION OF EIGENVALUES USING GRAPHICS PROCESSING UNITS},

   author={LUNGU, I. and P{^I}RJAN, A. and PETRO{c{S}}ANU, D.M.},

   year={2012}

}

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In this paper, we first briefly describe some mathematical aspects regarding the computation of eigenvalues, followed by an original approach: a bisection algorithm useful in computing eigenvalues for a tridiagonal symmetric matrix of arbitrary size, using the computing capabilities of the latest graphics processing units that incorporate the Compute Unified Device Architecture. The novel approach developed in this paper relates to an optimized algorithm’s implementation, based on the improvement of the shared memory management and on the increased efficiency of the scan algorithm. Thus, developers can use the huge parallel computational power offered by the Compute Unified Device Architecture.
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