TY - GEN A1 - Walter, Artur T1 - Improvement of Incomplete Factorizations by a Sparse Secant Method. N2 - In the present paper, the improvement of an incomplete factorization of a non-symmetric matrix A is discussed. Starting from the ideas of sparsity preserving quasi-Newton methods, an algorithm is developed which improves the approximation of A by the incomplete factorization maintaining the sparsity structure of the matrices. No renumbering of the unknowns or the admittance of additional fill-in is necessary. The linear convergence of the algorithm is proved under the assumption, that $ L $ and $ U $* have the same sparsity structure and an incomplete factorization with some reasonable approximation property exits. In combination with this algorithm, the method of incomplete factorization and its several modifications are applicable to a wider class of problems with improved convergence qualities. This is shown by a numerical example. {\bf Key Words:} non-symmetric linear system, sparse secant method, incomplete factorization. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20, 65N30. T3 - ZIB-Report - SC-90-12 KW - non-symmetric linear systems KW - sparse secant method KW - incomplete factorization Y1 - 1990 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/40 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-401 ER -