Given a set of scattered data with derivatives values, we use a minimal energy method to find Hermite interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. We show that the minimal energy method produces a unique Hermite spline interpolation of the given scattered data with derivative values. Also we show that the Hermite spline interpolation conve...

Dubuc’s interpolatory four-point scheme inserts a new point by fitting a cubic polynomial to neighbouring points over uniformly spaced parameter values. In this paper we replace uniform parameter values by chordal and centripetal ones. Since we update the parameterization at each refinement level, both schemes are non-linear. Because of this data-dependent parameterization, the schemes are only...

We consider finite element projection methods for linear partial differential equations, in which the spaces of trial functions and test functions may be different. In addition to approximation and smoothness properties, conditions implying equality of dimensions and uniform coerciveness are required, the most important of which resembles a strong form of an inverse assumption. Our results prov...

We present the explicit inverse of a class of symmetric tridiagonal matrices which is almost Toeplitz, except that the first and last diagonal elements are different from the rest. This class of tridiagonal matrices are of special interest in complex statistical models which uses the first order autoregression to induce dependence in the covariance structure, for instance, in econometrics or sp...

SUMMARY In many problems one wants to model the relationship between a response Y and a covariate X. Sometimes it is diicult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W which is easier to obtain. By far the most common model for the relationship between the actual covariate of interest X and the substitute W is W = X + U, where the v...

We present two new methods for approximating elevation data from contours to a grid. The first repeatedly interpolates new contour lines between the original ones. The second starts with any interpolated or approximated surface, determines its gradient lines, and does a Catmull-Rom spline interpolation along them to improve the elevations. We compare the new methods to a more classical thin-pla...

W e use a number of aggregate indicators to construct an index of market size for each of eight illicit drugs. These indices can be constructed routinely on an annual basis and are suitable as a baseline against which to judge the impact of anti-drugs policies. KEYW ORDS Illicit drug markets; latent variables; cubic spline trend JEL CLASSIFICATION C43, C82, K42 *I am grateful to John Corkery an...

A three-level method is proposed to achieve robust and real-time ball tracking in soccer videos. It includes object-, intra-trajectory-, and intertrajectory-level processing. Due to much noise and frequent occlusion, it’s difficult to get the solely ball in one frame. Thus, in object level, multiple objects instead of a single one are detected and taken as ball candidates with shape and color f...

software quality attribute and Software reliability estimation is a hard problem to solve accurately. However for management of software quality and standard practice of the organization, accurate reliability estimation is important. Non-homogeneous Poisson Process (NHPP) models and Artificial Neural Network (ANN) models are among the most important software reliability growth models. In this p...

In this paper we explore the use of recursive cubic Hermite splines to mimic human movement in open world games. Human-like movement in an open world environment has many characteristics that are not optimal or directed towards clear, discrete goals. Using data collected from a simple MMORPG-like game, we use our spline representation to model human player movements relative to corresponding op...