The parameter R2 in multiquadric interpolation

Using multiquadric quasi-interpolation for solving Kawahara equation

A Krylov subspace algorithm for multiquadric interpolation in many dimensions

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...

Applying Multiquadric Quasi-Interpolation to Solve KdV Equation

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’...

Solving partial differential equation by using multiquadric quasi-interpolation

In this paper, we use a kind of univariate multiquadric (MQ) quasi-interpolation to solve partial differential equation (PDE). We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the r...

A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters

A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (source points). The new approach clusters evaluation points instead and is therefore easily able to cope with basis functions that have different mul...