On quasi shift-splitting iteration method for a class of saddle point problems

Abstract

Motivated by a technique of scale-splitting for matrix, we put forward a quasi shift-splitting (named after QSS) iteration method to address a class of large scale sparse saddle point problems, this novel method also naturally leads to the corresponding QSS-preconditioner. In addition, an extrapolated variant of QSS (named after EQSS) iteration method is constructed. Further, some useful convergence properties of the QSS and EQSS iteration methods and spectral properties of QSS-preconditioner are studied. Finally, a saddle point equations stem from model Navier–Stokes problem is supplied to illustrate the effectiveness of our new two methods and QSS-preconditioner.