A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature, and algorithms are developed on a case by case basis. There lacks an analytical representation of a ge...

Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) and a trend function through sifting processes. For lack of a firm mathematical foundation, the implementation of EMD is still empirical and ad hoc. In this paper, we prove mathematically that EMD, as practiced now, only give...

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochasti...

The real root classification of a given parametric spline function is a collection of possible cases of its real root distribution on every interval, together with the conditions of its coefficients must be satisfied for each case. This paper presents an algorithm to deal with the real root classification of a given parametric spline function. Two examples are provided to illustrate the propose...

Third and fourth order convergent methods based on cubic nonpolynomial spline function at midknotes are presented for the numerical solution of a second order two-point boundary value problem with Neumann conditions. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. Convergence analysis of these methods is discussed t...

optimal balancing is a new approach based on optimal control a which modes, controls and the amount of equilibrium scale are calculated simultaneously. this approach has a significant effect on increasing performance of industrial robots which causes maximum decreasing of energy consumption. despite many applications of robotics such as welding and gluing, the path is predefined , but other unk...

In the present paper, the existence and uniqueness of deficient discrete cubic spline interpolant by matching the given function and first order difference at the intermediate points between successive mesh points for a uniform mesh has been discussed and also a error estimate concerning this deficient discrete cubic spline interpolant is obtained

Battle-Lemarié’s wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to `. The passing and stopping bands of the ideal filter are depende...

Splines are part of the standard toolbox for the approximation of functions and curves in Rd . Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be ...