Moreover, we apply the theory of weak continuity and weak convergence method to establish the asymptotical compactness of the processes.
Although this also does not guarantee local optimality, it has the advantage that its convergence is easy to establish, and it is a better approximation of the IFEM-1 algorithm than the high-SNR approximation.
Thus far, we have on one hand IFEM-1 and IFEM-2 algorithms, for which convergence is not easy to establish, but if they do converge, they converge to a local optimum.
This implies that x is an asymptotic center of ({x_{n_{k}}}), and hence ({ x_{n}}) Δ-converges to x. Chang et al. [11] established relations between the weak convergence and Δ-convergence in their attempt to establish the demiclosedness principle for total asymptotically nonexpansive mappings.
Convergence studies are performed to establish the stability and accuracy of the IMLS-Ritz method.
A systematic convergence study is conducted to establish the accuracy of the method for long time inviscid simulations.
Also, in this paper we present some useful properties of cone metric spaces, which allow us to establish convergence results for Picard iteration with a priori and a posteriori error estimates.
Also, in this section, we give some useful properties of cone metric spaces which allow us to establish convergence results for Picard iteration with a priori and a posteriori error estimates (Theorem 9.6 and Theorem 9.9).
The purpose of this paper is to establish convergence results of iteration process (3) for asymptotically nonexpansive mappings on a nonlinear domain ((UC) hyperbolic spaces) which includes both (UC) Banach spaces and CAT ( 0 ) spaces.
It is well known that α-SSS converges for any given (x^{(0)}) if and only if (rho(T <1), where (rho(T)) is the spectral radius of the matrix T. Thus, to establish convergence results for the α-SSS, we need to study the spectral radius of the iteration matrix in (7).
