Implementation On Iteration Algorithm For Fixed Point Of Nonlinear Operator

This article focused on the fixed point of several nonlinear operator on Hilbert space,Proposed several iterative algorithm which is easy to achieve on a computer, The strong convergences of these algorithms are proved. The main results of the paper obtained the following three aspects:Firstly, based on variational principle, we proposed an calculating method for the fixed point of contraction operator in separable Hilbert space. We use finite dimensional subspace successive approximation. This algorithm can be implemented directly on the computer. The numerical results show the effectiveness of the algorithm.Secondly, for the metric projection operator on finite closed convex subset in Hilbert space, we propose a relaxed alternate projection algorithm. Since this algorithm involves only to calculate the projection on the half the space series which contain a single closed convex subset. Therefore, the algorithm is easy to implement, numerical results show the effectiveness of the algorithm.Finally, for the Lipschitz strongly monotone variational inequalities in Hilbert space,we proposed an adaptive iterative algorithm based on the view of nonlinear operator, it wouldn't be necessary to calculate or estimate the Lipschitz constant and strongly monotone constants. Therefore, it is easy to implement.