TY - JOUR
ID - 244071
TI - Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Jamali, Hassan
AU - Kolahdouz, Mohsen
AD - Department of Mathematics, Faculty of Mathematics and Computer Sciences, Vali-e-Asr University of Rasanjan, Rafsanjan, Iran.
Y1 - 2021
PY - 2021
VL - 18
IS - 2
SP - 97
EP - 109
KW - Hilbert space
KW - Operator equation
KW - Frame
KW - Preconditioning
KW - Steepest descent method
KW - Convergence rate
DO - 10.22130/scma.2020.123786.771
N2 - In this paper, by using the concept of frames, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint linear operator on a separable Hilbert space $ H $. These schemes are analogous with steepest descent method which is applied on a preconditioned equation obtained by frames instead. We then investigate their convergence via corresponding convergence rates, which are formed by the frame bounds. We also investigate the optimal case, which leads to the exact solution of the equation. The first scheme refers to the case where $H$ is a real separable Hilbert space, but in the second scheme, we drop this assumption.
UR - https://scma.maragheh.ac.ir/article_244071.html
L1 - https://scma.maragheh.ac.ir/article_244071_85781e3d1440a36d832856bfda468567.pdf
ER -