A Kaczmarz-Kovarik algorithm for symmetric ill-conditioned matrices.

In this paper we describe an iterative algorithm for numerical solution of ill-conditioned inconsistent symmetric linear least-squares problems arising from collocation discretization of first kind integral equations. It is constructed by successive application of Kaczmarz Extended method and an appropriate version of Kovarik’s approximate orthogonalization algorithm. In this way we obtain a preconditioned version of Kaczmarz algorithm for which we prove convergence and make an analysis concerning the computational effort per iteration. Numerical experiments are also presented. AMS Subject Classification : 65F10 , 65F20. 1 Kaczmarz extended and Kovarik algorithms Beside many papers and books concerned with the qualitative analysis of classes of linear and nonlinear operators and operatorial equations, professor Dan Pascali also analysed the possibility to approximate solutions for some of them (see e.g. [5], [6]). This paper is written in the same direction, by considering iterative methods for numerical solution of first kind integral equations