On Skew-symmetric Preconditioning for Strongly Non-symmetric Linear Systems

Krukier, L.A. and Botchev, M.A. (1996) On Skew-symmetric Preconditioning for Strongly Non-symmetric Linear Systems. Zeitschrift für Angewandte Mathematik und Mechanik, 76 (Suppl.). pp. 483-484. ISSN 0044-2267

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Abstract:	To solve iteratively linear system $Au=b$ with large sparse strongly non-symmetric matrix $A$ we propose preconditioning $\hat A \hat u = \hat b$ , $\hat A=(I+\tau L_1)^{-1} A (I+\tau U_1)^{-1},\; \tau>0$ where respectively lower and upper triangular matrices $L_1$ and $U_1$ are so that $L_1+U_1=1/2(A-A^*)$ . Such preconditioning technique may be treated as a variant of ILU-factorization, and we call it MSSILU --- Modified Skew-Symmetric ILU. We investigate and optimize (with respect to $\tau$ ) convergence of preconditioned Richardson method (RM) of the following special form: ${\hat x}^{m+1}=(I-\tau \hat A){\hat x}^m+\tau {\hat b},\; m\geq 0$ , where $\tau$ is the same as in $\hat A$ . For this method we give an estimate for rate of convergence in relevant Euclidean norm for the case of positivereal matrix $A$ . Numerical experiments have included solving linear systems arising from 5-point FD approximation of convection--diffusion equation with dominated convection by MSSILU+RM, MSSILU+GMRES(2) and MSSILU+GMRES(10).
Item Type:	Article
Copyright:	© 2003 Wiley InterScience
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/65614
Official URL:	http://dx.doi.org/10.1002/zamm.19960761314
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