We investigate the approximation ability of a multilayer perceptron (MLP) network when it is extended to the complex domain. The main challenge for processing complex data with neural networks has been the lack of bounded and analytic complex nonlinear activation functions in the complex domain, as stated by Liouville's theorem. To avoid the conflict between the boundedness and the analyticity ...

In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

Several almost optimal results are obtained about N-term nonlinear approximation by dilated integer translates of a refinable function associated with a finite mask and a rather general matrix dilation A ∈ GLn(Z). §

Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree sturcture. This makes their positions eas...

This paper is concerned with the problem of nonlinear best simultaneous approximations in K?the Bochner function spaces respect to Minkowski? norms Euclidean spaces. Characterization results generalized approximation are established. These considered a generalization concerning Lebesgue and Orlicz

General analytical procedure for determination of the transverse feedback system parameters with a nonlinear regime of injection oscillations damping in circular accelerators and colliders is described. For this feedback loop the dependence between the kick value in the deflector and the beam deviation at the pick-up location is a nonlinear function. The beam dynamic nonlinear equation of the t...

The aim of the study presented in this paper is to provide some initial results over the potential use of best linear approximation models in the design of model-based linear controllers for systems suffering nonlinear distortions. This is illustrated on a nonlinear mechanical resonating system. Parametric best linear approximation models are estimated from frequency response function measureme...

We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and observation noise. The likelihood function is approximated by ridge function, i.e., map which depends nontrivially only on few linear combinations of the parameters. build this approximation minimizing an upper bound Kullback–Leibler divergence between posterior di...