HYBRID PROCEDURES FOR SOLVING LINEAR-SYSTEMS

In this paper, we introduce the notion of hybrid procedures for solvin g a system of linear equations. A hybrid procedure consists in a combi nation of two arbitrary approximate solutions with coefficients summin g up to one. Thus the combination only depends on one parameter whose value is chosen in order to minimize the Euclidean norm of the residua l vector obtained by the hybrid procedure. Properties of such procedur es are studied in detail. The two approximate solutions which are comb ined in a hybrid procedure are usually obtained by two iterative metho ds. Several strategies for combining these two methods together or wit h the previous iterate of the hybrid procedure itself are discussed an d their properties are analyzed. Numerical experiments illustrate the various procedures.