In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method,...

We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices...

We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and...