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Numerical Algorithms
Published in: Numerical Algorithms 4/2021

07-06-2020 | Original Paper

A new method for solving split equality problems via projection dynamical systems

Authors: Zengzhen Tan, Rong Hu, Yaping Fang

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

In this paper, we propose a projection dynamical system for solving the split equality problem, or more generally the approximate split equality problem, in Hilbert spaces. The proposed dynamical system endows with the continuous behavior with time for Moudafi’s alternating CQ-algorithm and Byrne and Moudafi’s extended CQ-algorithm. Under mild conditions, we prove that the trajectory of the dynamical system converges weakly to a solution of the approximate split equality problem as time variable t goes to \(+\infty \). We further derive the exponential-type convergence provided that a bounded linear regularity property holds for the approximate split equality problem. Several numerical examples are given to demonstrate the validity and transient behavior of the proposed method.
previous article Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation
next article A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations

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Metadata
Title
A new method for solving split equality problems via projection dynamical systems
Authors
Zengzhen Tan
Rong Hu
Yaping Fang
Publication date
07-06-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00950-5

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