In this paper, we present the convergence rate of the error in a neural network which was learnt by a constructive method. The constructive mechanism is used to learn the neural network by adding hidden units to this neural network. The main idea of this work is to nd the eigenvalues of the transformation matrix concerning the error before and after adding hidden units in the neural network. By...

Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...

The aim of this paper is to construct an e¢ cient iterative method to solve nonlinear equations. This method is obtained from M. Javidi’s method (Appl. Math. Comput. 193 (2007) 360-365), which is third-order. The convergence order of new method is established to six and the e¢ ciency index is 1.5651. The Proposed method is compared with the second, third and sixth order methods. Some numerical ...

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate ...

In this paper, we analyze the convergence of a second-order numerical method for the approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. Optimal convergence rate is derived. Numerical experiments are also reported to demonstrate the predicted accuracy of the scheme. Also, it is applied to solve a problem that d...

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...

Method for visualization of learning processes for back propagation neural network is proposed. The proposed method allows monitor spatial correlations among the nodes as an image and also check a convergence status. The proposed method is attempted to monitor the correlation and check the status for spatially correlated satellite imagery data of AVHRR derived sea surface temperature data. It i...

We consider learning convergence in Spiking Neural Networks trained according to the ReSuMe learning rule. We begin with a short introduction of the ReSuMe learning rules and we define the learning scenarios to be considered. Next, we present a formal proof of learning convergence for the Spike Response Model (SRM) trained according to the defined scenarios. Finally, we demonstrate that the pro...