Using Frames in Steepest Descent-Based Iteration Method for Solving Operator Equations
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)Publication Date: 2021-05-01
Authors : Hassan Jamali; Mohsen Kolahdouz;
Page : 97-109
Keywords : Hilbert space; Operator equation; Frame; Preconditioning; Steepest descent method; Convergence rate;
Abstract
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.
Other Latest Articles
- Two Equal Range Operators on Hilbert $C^*$-modules
- Second Module Cohomology Group of Induced Semigroup Algebras
- Some Properties of Complete Boolean Algebras
- Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}left( sright) $-Metric Spaces
- Joint Continuity of Bi-multiplicative Functionals
Last modified: 2021-11-03 14:32:34