Journal of the Ramanujan Mathematical Society

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Sparse Symmetric Indefinite Systems and Polynomial Preconditioning


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1 Department of Mathematics and Computer Science, Delaware State University Dover, Delaware 19901, United States
     

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In this paper, a new algorithm is proposed to solve indefinite symmetric sparse linear systems using polynomial preconditioning. The preconditioning polynomials are derived using simple calculus techniques. In practice, this algorithm, unlike other algorithms proposed in the literature, does not require complete knowledge of the intervals containing the spectrum of the given matrix. This method is superior to CG on normal equations, SYMMLQ, and Saad's GCI algorithm. Also the algorithm is amenable for implementing on parallel machines. The performance of the algorithm is compared with Saad's GCI algorithm on the minisupercomputer Alliant FX/8.
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  • Sparse Symmetric Indefinite Systems and Polynomial Preconditioning

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Authors

N. R. Nandakumar
Department of Mathematics and Computer Science, Delaware State University Dover, Delaware 19901, United States

Abstract


In this paper, a new algorithm is proposed to solve indefinite symmetric sparse linear systems using polynomial preconditioning. The preconditioning polynomials are derived using simple calculus techniques. In practice, this algorithm, unlike other algorithms proposed in the literature, does not require complete knowledge of the intervals containing the spectrum of the given matrix. This method is superior to CG on normal equations, SYMMLQ, and Saad's GCI algorithm. Also the algorithm is amenable for implementing on parallel machines. The performance of the algorithm is compared with Saad's GCI algorithm on the minisupercomputer Alliant FX/8.