Some projection-based direct solvers for general linear systems of equations

The Direct Projection-based solvers are direct methods for solving linear systems of equations in which an initial set of vectors are projected onto the hyperplanes of the system by using projections parallel with some specific directions also constructed during the development of the algorithm. They have been initially designed for square nonsingular systems, but further developments were produced also for more general ones (see an overview of these algorithms in [1], [6] and references therein). The main scope of our paper is to introduce and theoretically analyse a new class of such kind of direct solvers. Starting from some preliminary methods and results proposed by one of the authors in [15] we extend the theoretical analysis for one of them and design new block row and column projection versions. In the last section of the paper we use these algorithms and compare them with some classical direct projection-based ones for some numerical experiments on linear systems arising from rigid body dynamics problems.