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Reports (Research Report) Year : 1992

An Adaptive sparse unsymmetric linear system solver


Projection methods are the most widely used methods for computing a few of the extreme eigenvalues of large sparse matrices. Many of those algorithms have been turned out to solve linear systems of equations. In this paper we present an unsymmetric linear system solver based on projection techniques. We call this method adaptive because unlike usual Krylov subspace approximations which when receiving in entry an initial vector, they construct in a steady way a basis for the polynomial subspace where the approximated solution is sought, our approach follows up the construction process in order to enrich the basis with informations on the direction of the solution. Moreover it allows ad hoc actions to handle breakdowns internally. The convergence of the method is established when the symmetric part of the coefficient matrix is positive definite. Finally we illustrate the usefulness of the method using a number of representative PDE problems run on a Cray-2.


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Dates and versions

inria-00077028 , version 1 (29-05-2006)


  • HAL Id : inria-00077028 , version 1


Miloud Sadkane, Roger B. Sidje. An Adaptive sparse unsymmetric linear system solver. [Research Report] RR-1788, INRIA. 1992. ⟨inria-00077028⟩
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