Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) used for policy evaluation in reinforcement learning. Here, we consider TD with an additional heavy ball momentum term and provide choice step size parameter that ensures almost sure convergence these asymptotically. In doing so, decompose the iterates into three separate different sizes. ...

In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

the main objective of this paper is to study the boundedness character, the periodicity character, the convergenceand the global stability of the positive solutions of the nonlinear rational difference equation/ , n 0,1,2,....0 01      kii n ikin i n i x  x b  xwhere the coefficients i i b , ,  together with the initial conditions ,.... , , 1 0 x x x k  are arbitrary...

In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...

Correctness of many hybrid and distributed systems require stability and convergence guarantees. Unlike the standard induction principle for verifying invariance, a theory for verifying stability or convergence of automata is currently not available. In this paper, we formalize one such theory proposed by Tsitsiklis [25]. We build on the existing PVS metatheory for untimed, timed, and hybrid in...

The stability and convergence of fundamental numerical methods for solving ordinary differential equations are presented. These include one-step methods such as the classical Euler method, Runge–Kutta methods and the less well known but fast and accurate Taylor series method. We also consider the generalization to multistep methods such as Adams methods and their implementation as predictor–cor...

Renormalisation group techniques are important tools to describe how classical physics is modified by quantum fluctuations. Integrating-out all quantum fluctuations provides the link between the classical theory and the full quantum effective theory [1]. A useful method is given by the Exact Renormalisation Group (ERG) [2], which is based on the Wilsonian idea of integratingout infinitesimal mo...

A problem in differential equations can rarely be solved analytically, and so often is discretized, resulting in a discrete problem which can be solved in a finite sequence of algebraic operations, efficiently implementable on a computer. The error in a discretization is the difference between the solution of the original problem and the solution of the discrete problem, which must be defined s...