We consider the version of multiquadric interpolation where the interpolation conditions are the equations s(xi ) = fi , i = 1, 2, . . . , n, and where the interpolant has the form s(x) = ∑n j=1 λ j (‖x − x j‖ + c2)1/2 + α, x ∈ Rd , subject to the constraint ∑nj=1 λ j = 0. The points xi ∈ Rd , the right-hand sides fi , i = 1, 2, . . . , n, and the constant c are data. The equations and the cons...

Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations. Based on the good performance, Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation, which is generalized from the LD operator, and used it to solve hyperbolic conservation laws and Burgers’...

The total variation (TV) denoising method is a PDE-based technique that preserves the edges well but has undesirable staircase effect in some cases, namely, the translation of smooth regions (ramps) into piecewise constant regions (stairs). This paper introduces a novel mesh-free approach using TV (ROFmodel) regularization and radial basis function (RBF) for the numerical approximation of TV-ba...

The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order (1 ≤ p ≤ ∞) of interpolatio...

This paper presents a statistical decision procedure for lexical ambiguity resolution. The algorithm exploits both local syntactic patterns and more distant collo-cational evidence, generating an eecient, eeective, and highly perspicuous recipe for resolving a given ambiguity. By identifying and utilizing only the single best dis-ambiguating evidence in a target context, the algorithm avoids th...

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...