For a time-independent Schrödinger equation with Hamiltonian operator H = −∆ + V on L(R ) we call Gz = RzV , the Green function operator, where Rz is the resolvent of −∆. We consider an iteration scheme that is based on the operator Gz. Under standard conditions on the potential V , which include the Coulomb interaction, we prove the convergence of the iteration to the ground state energy and e...

The aim of this article is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed point for generalized asymptotically quasi-nonexpansive mappings and also establish a weak convergence theorem by using Opial’s [11] condition for said iteration scheme and mappings in the framework of Banach spaces. The results presented in this pa...

The paper is concerned with the solution of nonlinear ill-posed problems by methods that utilise the second derivative. A general predictor{corrector approach is developed; one which avoids solving quadratic equations during the iteration process. Combining regularisation of each iteration step with an adequate stopping condition leads to a general regularisation scheme for nonlinear equations....

In this paper, we establish a weak convergence theorem and some strong convergence theorems of an explicit iteration process for a finite family of strictly asymptotically pseudo-contractive mappings in the intermediate sense and also establish a strong convergence theorem by a new hybrid method for above said iteration scheme and mappings in the setting of Hilbert spaces. AMS Mathematics Subje...

In this paper, we prove the strong convergence of an implicit iterative scheme with errors to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings in convex metric spaces. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces. With the help of an example we compare implicit iteration used in our re...

In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through -convergence and strong convergence under some weaker conditions. A necessary...

We describe a point-based approximate value iteration algorithm for partially observable Markov decision processes. The algorithm performs value function updates ensuring that in each iteration the new value function is an upper bound to the previous value function, as estimated on a sampled set of belief points. A randomized belief-point selection scheme allows for fast update steps. Results i...

*Correspondence: [email protected] 1College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, P.R. China Abstract In this paper, we propose an iteration method for finding a split common fixed point of asymptotically nonexpansive semigroups in the setting of two Banach spaces, and we obtain some weak and strong convergence theorems of the itera...

A recursive self-tuning control scheme for finite Markov chains is proposed wherein the unknown parameter is estimated by a stochastic approximation scheme for maximizing the log-likelihood function and the control is obtained via a relative value iteration algorithm. The analysis uses the asymptotic o.d.e.s associated with these.

The aim of this paper is to analyse the gain of the update algorithm associated to the recently proposed D-iteration: the D-iteration is a fluid diffusion based new iterative method. It exploits a simple intuitive decomposition of the product matrix-vector as elementary operations of fluid diffusion (forward scheme) associated to a new algebraic representation. We show through experimentations ...