VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

Study on divertor heat flux under n=3 and n=4 resonant magnetic perturbations using infrared thermography diagnostic in EAST

Resonant magnetic perturbations(RMPs)with high toroidal mode number n are considered for controlling edge-localized modes(ELMs)and divertor heat flux in future ITER H-mode operations.In this paper,characteristics of divertor heat flux under high-nRMPs(n=3 and 4)in H-mode plasma are investigated using newly upgraded infrared thermography diagnostic in EAST.Additional splitting strike point(SSP)accompanying with ELM suppression is observed under both RMPs with n=3 and n=4,the SSP in heat flux profile agrees qualitatively with the modeled magnetic footprint.Although RMPs suppress ELMs,they increase the stationary heat flux during ELM suppression.The dependence of heat flux on q_(95)during ELM suppression is preliminarily investigated,and further splitting in the original strike point is observed at q 495=during ELM suppression.In terms of ELM pulses,the presence of RMPs shows little influence on transient heat flux distribution.

A new alternating positive semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models

Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.

Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these Mgorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the Mgorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.

Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces

In this paper,we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces.We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions.As an application,the results are applied to solving the zero problem and the equilibrium problem.

Inference for Optimal Split Point in Conditional Quantiles

In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.