By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

We proposed the I-spline Smoothing approach for calibrating predictive models by solving a nonlinear monotone regression problem. We took advantage of I-spline properties to obtain globally optimal solutions while keeping the computational cost low. Numerical studies based on three data sets showed the empirical evidences of I-spline Smoothing in improving calibration (i.e.,1.6x, 1.4x, and 1.4x...

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (Battle-Lemarié), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-DaubechiesFeauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates...

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. The spline kernels are useful for continuous signal processing algorithms that involve Bspline inner-products or the convolution of several spline basis functions. We apply our results to the derivation of spline-based algorithms for two classes of p...

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

Changing the aspect-ratio (scale) of a graphical plot significantly affects the "messages" getting across to a viewer. This is true also for curvature plots and other graphs currently used in Curve & Surface Modeling to evaluate fairness. In particular, the sharp corners appearing in such graphs, employed as local.fairness indicators by current practices, are significantly affected by nonunifor...

In many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. Since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, GIS-based modeling approach was utilized to zoning PM2.5 dispersion over Tehran, du...

The Gaussian function G(x) = 1 p 21⁄4 e¡x 2=2; which has been a classical choice for multiscale representation, is the solution of the scaling equation G(x) = Z R ®G(®x¡ y)dg(y); x 2 R; with scale ® > 1 and absolutely continuous measure dg(y) = 1 p 21⁄4(®2 ¡ 1) e¡y 2=2(®2¡1)dy: It is known that the sequence of normalized B-splines (Bn); where Bn is the solution of the scaling equation Á(x) = n ...

The growing interest in image scaling is mainly due to the availability of digital imaging devices such as, digital video cameras, digital camcorders, 3G mobile handsets, high definition monitors etc. Scaling a digital image is a demanding and very important area of research. The grid based image scaling technique is proposed, where grid size equals the new desired dimensions of digital image. ...