作者：薛中会

作者单位：河南理工大学物理与电子信息学院

摘要：分裂共同半压缩映射不动点问题是一类比较经典的问题模型,目前算法多是运用当前迭代点的信息构建新的迭代点,这类算法收敛比较慢,且仅具有线性收敛性。为构建快速有效算法,受惯性近似算法求解极大单调算子零点问题的启发,针对半压缩映射的共同分裂不动点问题,通过引入惯性因子,提出一种具有二次收敛性的惯性迭代算法,并在适当条件下证明了算法的渐近收敛性。惯性技术的应用能提高迭代序列的收敛速率,减少迭代步数,从而大大减少计算量。

Abstract：Split common fixed-point problem for demicontractive mappings is a classic problem model. Currently, most algorithms employ existed point to obtain the next iterate which leads to slow convergence (only linear convergence) . In order to construct fast and valid algorithm, the inertial proximal algorithm is inspired to find zero of a maximal monotone operator. In this paper, an inertial iteration algorithm is proposed to solve the split common fixed point problem for demicontractive mappings by introducing a inertial factor. The asymptotical convergence of the algorithm is also proved under some suitable conditions. The algorithm constructed by applying inertial technique can improve convergence rate of the iterative sequence.

关键词：分裂共同不动点问题;惯性技术;半压缩映射;渐进收敛;

DOI：10.16186/j.cnki.1673-9787.2018.02.021

分类号：O177.91