It often happens that iteration processes used for solving the implicit relations arising in ODE-IVP methods only start to converge rapidly after a certain number of iterations. Fast convergence right from the beginning is particularly important if we want to use so-called step-parallel iteration in which the iteration method is concurrently applied at a number of step points. In this paper, we...

Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary ini...

A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

The Waterfall model has dominated software development for many years, but iteration of processes is catching in. There is now a number of well-established iterative development process models that can be classified according to the levels where iteration is applied. Iteration can improve validation and verification by allowing earlier quality feedback. Moreover, there seems to be a secret marr...

This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonalimplicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is ^(a)-stable or Z,(a)-stable with a e...

For solving linear ill-posed problems, regularizationmethods are requiredwhen the right-hand side is with some noise. In this paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. By exploiting operator monotonicity of certain functions and interpolation techniques in variable Hilbert scales, we study these methods under general smoothness conditions. Order o...

We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the sur...

We introduce iteration in process algebra by means of (the binary version of) Kleene's star operator: x y is the process that chooses between x and y, and upon termination of x has this choice again. It is proved that adding respectively interleaving, communication and abstraction operators increases expressivity up to the regular processes. However, if the distinction between (successful) term...