Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors
The authors consider several preconditioners for iterative solution methods. The preconditioners are based on incomplete direct methods. One method, called the generalized approximate inverse matrix technique, is based on a construction of the inverse of an \(n\times n\) matrix A starting from the factorization \(A=LU\), but without computing \(L^{-1}\) and \(U^{-1}\) explicitly. This method, and a variant based on retaining only some of the diagonals of the inverse, can be efficiently computed by diagonals on a vector or parallel processor. A second class of methods is based on Gauss-Jordan elimination and the resulting expression of \(A^{-1}\) as a product of simple matrices. The different methods in the class are determined by retention of different numbers of diagonals. Numerical results are presented for several different variations of these methods applied to the matrix arising from a ``2D-model problem''. The model problem is not described.
generalized approximate inverse matrix technique
scientific article; zbMATH DE number 4016029
scientific article