The purpose of this article is to initiate the notion monotone multivalued generalized (α,β)-nonexpansive mappings and explore iterative approximation fixed points for mapping in an ordered CAT(0) space. In particular, we employ S-iteration algorithm space prove some convergence results. Moreover, examples useful results related proposed are provided. Numerical experiments also provided illustr...

We present a linear iteration algorithm to implement a second-order energy stable numerical scheme for amodel of epitaxial thin film growth without slope selection. The PDE, which is a nonlinear, fourth-order parabolic equation, is the L2 gradient flow of the energy ∫ ( − 1 2 ln ( 1+ |∇φ|2+ 2 2 | φ(x)|2 ) dx. The energy stability is preserved by a careful choice of the second-order temporal app...

This paper presents an a posteriori error estimator for the preconditioned iteration scheme of Bramble, Knyazev and Pasciak to compute the smallest eigenvalues together with its invariant subspace of an elliptic diierential operator. The error estimator is applied both to the nite element space in which the preconditioned iteration is performed (iteration error estimation) as well as to its hie...

Inverse iteration, if applied to a symmetric positive definite matrix, is shown to generate a sequence of iterates with monotonously decreasing Rayleigh quotients. We present sharp bounds from above and from below which highlight inverse iteration as a descent scheme for the Rayleigh quotient. Such estimates provide the background for the analysis of the behavior of the Rayleigh quotient in cer...

In this paper, we introduce a new subdivision scheme which we call honeycomb subdivision. After one iteration of the scheme each vertex becomes exactly 3-valent and with consecutive applications regular regions strongly resembles a honeycomb. This scheme can be considered as a dual for triangle schemes. The major advantage of the new scheme is that it creates a natural looking mesh structure.

A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlappin...

In this work, a revised iterative learning control based ramp metering algorithm with compensation for the iteration-depended traffic free speed is proposed. This control method works well when free speed is iteration-varying, which is the most common situation for the freeway traffic system. With rigorous analysis, the proposed control scheme guarantees the asymptotic convergences along the it...