TY - JOUR
ID - 31814
TI - Richardson and Chebyshev Iterative Methods by Using G-frames
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Jamali, Hassan
AU - Kolahdouz, Mohsen
AD - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Y1 - 2019
PY - 2019
VL - 13
IS - 1
SP - 129
EP - 139
KW - Hilbert space
KW - G-Frame
KW - Operator equation
KW - Iterative method
KW - Chebyshev polynomials
DO - 10.22130/scma.2018.68917.266
N2 - In 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.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. 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.
UR - https://scma.maragheh.ac.ir/article_31814.html
L1 - https://scma.maragheh.ac.ir/article_31814_ef793a9c97fed9f9c9716480c9dad7d0.pdf
ER -