Composite adaptive procedure for solving large sparse linear systems
Adapted from the author's abstract: A large number of iterative algorithms for solving the matrix equation \(Ax=b\) have been developed in recent years. Some of these involve ``splitting parameters'', for example the relaxation parameter in the symmetric overrelaxation method, which are sensitive to their values. These can seldom be determined accurately in advance, and adaptive procedures are often used. A number of such procedures have been developed for finding the optimum splitting parameter for some iterative methods which are only applicable for some special cases. In the present paper a general adaptive procedure is given. This is similar to the ORTHONORM generalized conjugate gradient algorithm of \textit{D. M. Young} and \textit{K. C. Jea} [ibid. 34, 159-194 (1980; Zbl 0463.65025)] and is based on the minimization of an appropriate quadratic form using a unimodal search procedure. Computational algorithms are presented. There is a section on some numerical experiments for some problems which arise from solving partial differential equations. The author discusses briefly the parallelization of the methods.
scientific article; zbMATH DE number 4213318
scientific article