We consider the problem of acceleration of the Alternative Directions Implicit (ADI) scheme for Dirichlet problem for biharmonic equation. The second Douglas scheme is used as the main vehicle and two full time steps are organised in a single iteration unit in which the explicit operators are arranged differently for the second step. Using an a priori estimate for the spectral radius of the ope...

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration...

By making use of tools from convex analysis, we formulate an inexact NewtonLandweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme provides increments by applying Landweber iteration with non-smooth uniformly convex penalty terms to local linearized equations. The o...

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexp...

Within the setting of the categorical approach to total functional programming, we introduce a \many-in-one" recursion scheme that neatly uniies a variety of seemingly diverging strengthenings of the basic recursion scheme of iteration. The new scheme is doubly generic: in addition to being parametric in a functor capturing the signature of an inductive type, it is also parametric in a comonad ...

In this paper, we draw upon connections between bilinear programming and the process of computing (post) fixed points in abstract interpretation. It is well-known that the data flow constraints for numerical domains are expressed in terms of bilinear constraints. Algorithms such as policy and strategy iteration have been proposed for the special case of bilinear constraints that arise from temp...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...