The Taylor series expansion of continuous functions has shown in many fields to be an extremely powerful tool to study the characteristics of such functions. This paper illustrates the power of the Taylor series expansion of multilayer feedforward neural networks. The paper shows how these expansions can be used to investigate positions of decision boundaries, to develop active learning strateg...

Online Appendix In this online appendix, I first provide a brief comparison of the small noise expansion series and the Taylor expansion series. I then use separably Taylor expansion series and the small noise expansion series to derive the pricing kernel in a one-market model with two dates, and the pricing kernel in a two-market model with three dates. I thereafter, investigate whether one ob...

This paper describes a design based o n the Taylor series to approximate a function and its derivatives. A f ter being trained, derivatives are obtained in a fast feed forward evaluation without the need fo r backpropagation or fornard perturbation. The Taylor network is basically a n implementation of the Taylor series of a function. However, instead of only having one expansion point, it uses...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

For a large class of two-loop selfenergyand vertex-type diagrams with only one nonzero mass (M) and the vertices also with only one non-zero external momentum squared (q2) the first few expansion coefficients are calculated by the large mass expansion. This allows to ‘guess’ the general structure of these coefficients and to verify them in terms of certain classes of ‘basis elements’, which are...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.