Richardson and Chebyshev Iterative Methods by Using G-frames
In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow 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-st...
| Published in: | Sahand Communications in Mathematical Analysis |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2019-02-01
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| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_31814_ef793a9c97fed9f9c9716480c9dad7d0.pdf |
| Summary: | In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow 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. |
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| ISSN: | 2322-5807 2423-3900 |