SOLVING POSITIVE (SEMI)DEFINITE LINEAR-SYSTEMS BY PRECONDITIONED ITERATIVE METHODS

The use of preconditionings obtained by so called modified incomplete factorizations has become quite popular for the PCG solution of regular systems arising from the discretization of elliptic PDE's. Our purpose here is to review their recent extension to the singular case. Because such conditionings may themselves be singular, we first review the extension of the general theory of polynomial acceleration to the case of singular preconditionings. We emphasize that all results can be formulated in such a way that they cover both the regular and singular cases. Examples of application are given, displaying the superiority of the recently developed factorization strategies.