Preconditioning projection methods for solving algebraic linear systems (Q1817786)

The author devises a method for finding appropriate parameters for an \(n\times n\) matrix \(M\) through a link with the conjugate gradient method and a sequence of \(m\times 1\) vectors \(\{u_i\}_{i=1}^\infty\) to improve the convergence of the projection aggregation method for solving a consistent linear system of \(n\) variables and \(m\) equations \((m\geq n)\). It is found that the applications of these results to a hard \(3D\) partial differential equations are highly promising. Finally the method is adapted to the solution of a system of linear inequalities.