Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for approximation by linear combinations of nonuniform translates of the Sobolev splines. Our results extend previous work as we obtain rates for ba...

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...

In this paper, we present an easy and e cient method for computing the range of a function by using spline quasi-interpolation. We exploit the close relationship between the spline function and its control polygon and use tight subdivision technique in order to obtain monotonic splines which make the range of the spline easy to compute. The proposed method is useful in case of given scattered d...

Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form Z× aZn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines Ia on such grids for the limiting process a → 0, a > 0. For a l...

A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integra...

A well-known approach to image interpolation is cubic convolution, in which the ideal sinc function is modelled by a finite extent kernel, which consists of piecewise third order polynomials. In this paper we show that the concept of cubic convolution can be generalized. We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders. From s...

In many situations we have to fill one or several holes of certain function defined in a domain where there is a lack of information inside some sub-domains. For this we have developped some methods (see [1, 2, 3, 4]). But in some practical cases we just know some specific geometrical constraints, of industrial or design type, as the special case of a specified volume inside each one of these s...

This paper concerns the fast evaluation of radial basis functions. It describes the mathematics of hierarchical and fast multipole methods for fast evaluation of splines of the form

This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key strategy is linear space embedding with the operator of mixed partial derivative. The dimension of the original space equals the difference between the dimension o...