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The Landweber Operator Approach to the Split Equality Problem

The split equality problem (SEP) seeks a pair of points $(x^{\ast },y^{\ast })\in (C,D)$ with the property that $Ax^{\ast }=By^{\ast }$, where $C,D$ are nonempty closed convex subsets of Hilbert spaces $\mathcal{H}_{1}$ and $% \mathcal{H}_{2}$, respectively, and $A:\mathcal{H}_{1}\rightarrow \mathcal{H}% _{3}$ and $B:\mathcal{H}_{2}\rightarrow \mathcal{H}_{3}$ are bounded linear operators, where $\mathcal{H}_{3}$ is another Hilbert space. The SEP can equivalently be converted to a split feasibility problem in the product space $\mathcal{H}_{1}\times \mathcal{H}_{2}$. Using this equivalence, we are able to provide a Landweber operator approach to studying the convergence of several iterative methods for finding a solution to the SEP. We also discuss the linear regularity of the Landweber operator associated with the SEP and linear convergence of the iterative methods.


Read More: https://epubs.siam.org/doi/abs/10.1137/20M1337910

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Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.1 January-March 2021

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 626 - 652

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

NONEXPANSIVE MAPPING
LINEAR CONVERGENCE
LINEAR REGULARITY
LANDWEBER OPERATOR
AVERAGED MAPPING, PROJECTION
SPLIT FEASIBILITY
SPLIT EQUALITY

Info Detail Spesifik

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Pernyataan Tanggungjawab

Hong-Kun Xu, Andrzej Cegielski

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