Related to the speed of the time response is the convergence rate, which can be determined using invariant sets.
Here, we use our new idea of recurrent functions in order to provide new sufficient convergence conditions, which can be weaker than before [4].
It can be proved to have the property that the modified Bregman method is equivalent to the corresponding accelerated augmented Lagrangian method, and the latter has a rapid convergence rate which can be deemed to be an improvement of [17].
The main purpose of this paper is to establish the Khintchine-Kolmogorov-type convergence theorem, which can be applied to obtain the three series theorem and the Chung-type strong law of large numbers for ψ-mixing random variables.
Hence, ({x_{n}}) does not converge to a fixed point of T. Based on Lemma 3.6 ii), we present a convergence theorem which can be reduced to the Mann algorithm.
The Nash equilibrium can be deemed to be achieved when ψ(x(K), y)<ε after multiple iterations, where K is the number of iterations and ε is the convergence precision which can be set as a relatively small positive number.
In this paper, by using the Rosenthal-type maximal inequality for ψ-mixing random variables, we obtain the Khintchine-Kolmogorov-type convergence theorem, which can be applied to establish the three series theorem and the Chung-type strong law of large numbers for ψ-mixing random variables.
The high resolution and positivity preservation of the proposed discretization stencils are independent of the convergence acceleration technique which can be set to multigrid, preconditioning, Jacobian-free Newton Krylov, block-implicit, etc.
