Conditioning analysis of block incomplete factorization and its application to elliptic equations

Lu, Hao and Axelsson, Owe (1997) Conditioning analysis of block incomplete factorization and its application to elliptic equations. Numerische Mathematik, 78 (2). pp. 189-209. ISSN 0029-599X

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Abstract:	The paper deals with eigenvalue estimates for block incomplete fac- torization methods for symmetric matrices. First, some previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue. Second, upper bounds for the maximum eigenvalue of the preconditioned matrix are further estimated, which presents a substantial im- provement of earlier results. Finally, the results are used to estimate bounds for every eigenvalue of the preconditioned matrices, in particular, for the maximum eigenvalue, when a modified block incomplete factorization is used to solve an elliptic equation with variable coefficients in two dimensions. The analysis yields a new upper bound of type γh−1 for the condition number of the preconditioned matrix and shows clearly how the coefficients of the differential equation influ- ence the positive constant γ.
Item Type:	Article
Copyright:	© 1997 Springer
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/73764
Official URL:	http://dx.doi.org/10.1007/s002110050310
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