A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

This report describes a technique to detect curvature. The technique uses local polynomial fitting on a local orientation description of an image. The idea is based on the theory of rotational symmetries which describes curvature, circles, starpatterns etc. The local polynomial fitting is shown to be equivalent to calculating partial derivatives on a lowpass version of the local orientation. Th...

TheMultiscale Local Polynomial Transform (MLPT), developped in this paper, combines the benefits from local polynomial smoothing with sparse multiscale decompositions. The contribution of the paper is twofold. First, it focusses on the bandwidths used throughout the transform. These bandwidths operate as user controlled scales in a multiscale analysis, which is explained to be of particular int...

This paper is concerned with an interior penalty discontinuous Galerkin (IPDG) method based on a flexible type of non-polynomial local approximation space for the Helmholtz equation with varying wavenumber. The local approximation space consists of multiple polynomial-modulated phase functions which can be chosen according to the phase information of the solution. We obtain some approximation p...

A discrete polynomial curve is defined as a set of points lying between two polynomial curves. This paper deals with the problem of fitting a discrete polynomial curve to given integer points in the presence of outliers. We formulate the problem as a discrete optimization problem in which the number of points included in the discrete polynomial curve, i.e., the number of inliers, is maximized. ...