A new approach to convergence analysis of iterative models with optimal error bounds
Fuente:
arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917558251159552 |
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| author | Tran, Minh-Phuong Nguyen, Thanh-Nhan Nguyen, Thai-Hung Nguyen, Tan-Phuc Nguyen, Tien-Khai Nguyen, Cong-Duy-Nguyen Huynh, Trung-Hieu |
| author_facet | Tran, Minh-Phuong Nguyen, Thanh-Nhan Nguyen, Thai-Hung Nguyen, Tan-Phuc Nguyen, Tien-Khai Nguyen, Cong-Duy-Nguyen Huynh, Trung-Hieu |
| contents | In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new approach to convergence analysis of iterative models with optimal error bounds Tran, Minh-Phuong Nguyen, Thanh-Nhan Nguyen, Thai-Hung Nguyen, Tan-Phuc Nguyen, Tien-Khai Nguyen, Cong-Duy-Nguyen Huynh, Trung-Hieu Numerical Analysis In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings. |
| title | A new approach to convergence analysis of iterative models with optimal error bounds |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.02093 |