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- 저자 : Davod K. Salkuyeh (검색결과 2 건)
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BILUS: a block version of ILUS factorization
Davod K. Salkuyeh,Faezeh Toutounian 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
ILUS factorization has many desirable properties such as itsamenability to the skyline format, the ease with which stability may bemonitored, and the possibility of constructing a preconditioner with sym-metric structure. In this paper we introduce a new preconditioning tech-nique for general sparse linear systems based on the ILUS factorizationstrategy. The resulting preconditioner has the same properties as the ILUSpreconditioner. Some theoretical properties of the new preconditioner arediscussed and numerical experiments on test matrices from the Harwell-Boeing collection are tested. Our results indicate that the new precondi-tioner is cheaper to construct than the ILUS preconditioner.
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Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic
F. Toutounian,,Davod K. Salkuyeh,Bahram Asadi 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors vn+1 and wn+1 as regular or inner vectors. For a regular step it is necessary that Dk = WT k Vk is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix Dk, min(Dk), is computed and an inner step is performed if min(Dk) < , where is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance . The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.
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