Convergence Rate Analysis of Inertial Krasnoselskii-Mann Type Iteration with Applications
It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii-Mann it...
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| Vydáno v: | Numerical functional analysis and optimization Ročník 39; číslo 10; s. 1077 - 1091 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Abingdon
Taylor & Francis
27.07.2018
Taylor & Francis Ltd |
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| ISSN: | 0163-0563, 1532-2467 |
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| Abstract | It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic
convergence rate result for a Krasnoselskii-Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas-Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii-Mann iteration in the literature. |
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| AbstractList | It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic
convergence rate result for a Krasnoselskii-Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas-Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii-Mann iteration in the literature. It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic [Formula omitted.] convergence rate result for a Krasnoselskii-Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas-Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii-Mann iteration in the literature. |
| Author | Shehu, Yekini |
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| SubjectTerms | Convergence Convergence rate Hilbert space Hilbert spaces inertial terms Iterative methods nonexpansive mapping Operators (mathematics) |
| Title | Convergence Rate Analysis of Inertial Krasnoselskii-Mann Type Iteration with Applications |
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