A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex...

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...

Nacrtak This paper describes a program for optimizing forest road alignments using the Dijkstra shortest path method and a cubic spline function. We previously developed a method for optimizing forest road alignments once a series of intersection points (IPs) were selected manually using Tabu Search. The application of the program to a part of Capitol State Forest in Washington State, USA indic...

This paper aims to obtain approximate solutions of the one-dimensional nonlinear Klein-Gordon equation by employing Cubic B-spline wavelets. Our scheme uses the Galerkin method and approximates the solution in the terms of cubic B-spline scaling and wavelet functions. These wavelets are applied as testing and weighting functions. Because of some properties of these wavelets such as having compa...

This paper presents an eecient algorithm to generate realistic images using spline wavelets. Our algorithm departs from the use of non-overlapping wavelets by providing a continuous solution at no extra cost. This in turn eliminates need for inaccurate Gouraud shading or expensive nal gather step. Advantage of spline wavelets come from the fact that scaling functions are n th order B-splines th...

We propose a new regularization method called Loco-Spline for nonparametric function estimation. Loco-Spline uses a penalty which is data driven and locally adaptive. This allows for more flexible estimation of the function in regions of the domain where it has more curvature, without over fitting in regions that have little curvature. This methodology is also transferred into higher dimensions...

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

B-spline scaling functions and wavelets have found wide applicability in many scientific and practical problems thanks to their unique properties. They show considerably better results in comparison to other wavelets, and they are used as well in mathematical approximations, signal processing, image compression, etc. But only the first four wavelets from this family were mathematically formulat...

In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

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...