Based on the general inner-outer (GIO) iteration method [5,34] and framework [6], we present a multi-step matrix splitting (GMMS) for computing PageRank, analyze its overall convergence property. Moreover, same idea can be used as preconditioning technique accelerating Krylov subspace methods, such GMRES method. Finally, several numerical examples are given to illustrate effectiveness of propos...

It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...

Orbital minimization is among the most promising linear scaling algorithms for electronic structure calculation. However, to achieve linear scaling, one has to truncate the support of the orbitals and this introduces many problems, the most important of which is the occurrence of numerous local minima. In this paper, we introduce a simple modification of the orbital minimization method, by addi...

In this paper, several $Delta$ and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results