University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Richardson and Chebyshev Iterative Methods by Using G-frames1291393181410.22130/scma.2018.68917.266ENHassanJamaliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.MohsenKolahdouzDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20170727In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:H\rightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern, Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.<br />In this paper, these schemes exploit the almost recently developed notion of g-frames which result in modified convergence rates compared with early computed ones in corresponding classical formulations. <br />In fact, these convergence rates are formed by the lower and upper bounds of the given g-frame. Therefore, we can determine any convergence rate by considering an appropriate g-frame.https://scma.maragheh.ac.ir/article_31814_ef793a9c97fed9f9c9716480c9dad7d0.pdf