In this article, we present an error estimate of the derivative approximation by the local multiquadricbased differential quadrature (LMQDQ) method. Radial basis function is different from the polynomial approximation, in which Taylor series expansion is not applicable. So, the present analysis is performed through the numerical solution of Poisson equation. It is known that the approximation e...

In this paper, the Neumann-Dirichlet boundary problem for a system of nonlinear viscoelastic equations Kirchhoff type with Balakrishnan-Taylor term is considered. At first, local existence established by linear approximation together Faedo- Galerkin method. Then, establishing several reasonable conditions and suitable energy inequalities, solution admits general decay in time.

We consider the problem of interpolating scattered data using spline methods and present a general framework of using the multipole method to accelerate the evaluation of splines. The method depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation. We also illustrate the performance of the ...

This paper presents an alternative means of deriving and discretizing spectral distances and kernels on a 3D shape by filtering its Laplacian spectrum. Through the selection of a filter map, we design new spectral kernels and distances, whose smoothness and encoding of both local and global properties depend on the convergence of the filtered Laplacian eigenvalues to zero. Approximating the dis...

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant ...

We propose likelihood and restricted likelihood ratio tests for goodness-of-fit of nonlinear regression. The first order Taylor approximation around the MLE of the regression parameters is used to approximate the null hypothesis and the alternative is modeled nonparametrically using penalized splines. The exact finite sample distribution of the test statistics is obtained for the linear model a...

In our previous work, we proposed a feature compensation approach using high-order vector Taylor series approximation for noisy speech recognition. In this paper, first we improve the feature compensation in both efficiency and accuracy by boosted mixture learning of GMM, applying higher order information of VTS approximation only to the noisy speech mean parameters, acoustic context expansion,...

This paper presents a speech enhancement approach derived by using a piecewise linear approximation (PLA) of an explicit model of environmental distortions. PLA is a generalization of two traditional approaches, namely vector Taylor series (VTS) and MAX approximations. Formulations are described for both maximum likelihood (ML) estimation of noise model parameters and minimum mean-squared error...

A treecode algorithm is presented for rapid computation of the nonbonded potential energy in classical molecular systems. The algorithm treats a general form of pairwise particle interaction with the Coulomb and London dispersion potentials as special cases. The energy is computed as a sum of group–group interactions using a variant of Appel’s recursive strategy. Several adaptive techniques are...

With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...