Abstract Given gridded cell-average data of a smooth multivariate function, we present constructive explicit procedure for generating high-order global approximation the function. One contribution is derivation approximations to point-values function directly from data. The second development univariate B-spline-based quasi-interpolation operators using Multivariate spline are obtained by tenso...

In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. Th...

This paper generalizes the classical spline using a new construction of spline coalescence hidden variable fractal interpolation function (CHFIF). The derivative of a spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of a nondiagonal iterated function system. Our construction generalizes the construction of Barnsley and Harrington (198...

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to L are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule. Key...

Battle-Lemarie wavelet systems of natural orders are established in the paper. The main result work is decomposition theorem Besov and Triebel-Lizorkin spaces with local Muckenhoupt weights, which performed terms bases generated by such a type. wavelets splines suit very well for study integration operators.

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

To de ne spline subdivision schemes for general compact sets we use the representation of spline subdivision schemes in terms of repeated averages and replace the usual average convex combination by a binary averaging operation between two compact sets introduced in and termed here the metric average These schemes are shown to converge in the Hausdor metric and to provide O h approximation x In...