A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

A Python Script for Geometric Interval Classification in QGIS: A Useful Tool for Archaeologists

Graduated colour maps, created through the mathematical classification of quantitative variables, are frequently used in archaeology. A Python script for implementing a classification method based on geometric intervals in QGIS is presented here. This method is more suitable than the standard methods in case the quantitative attribute to be classified follows a right-skewed distribution, which is common among archaeological data. After an overview of the main classification methods, this paper focuses on the benefits of the geometric interval subdivision scheme, describes the technical features of the script and demonstrates how it works. A final thought on the advantages of using FLOSS is proposed.

Subdivision Collocation Method for One-Dimensional Bratu’s Problem

The purpose of this article is to employ the subdivision collocation method to resolve Bratu’s boundary value problem by using approximating subdivision scheme. The main purpose of this researcher is to explore the application of subdivision schemes in the field of physical sciences. Our approach converts the problem into a set of algebraic equations. Numerical approximations of the solution of the problem and absolute errors are compared with existing methods. The comparison shows that the proposed method gives a more accurate solution than the existing methods.

Analysis of a New Nonlinear Interpolatory Subdivision Scheme on σ Quasi-Uniform Grids

In this paper, we introduce and analyze the behavior of a nonlinear subdivision operator called PPH, which comes from its associated PPH nonlinear reconstruction operator on nonuniform grids. The acronym PPH stands for Piecewise Polynomial Harmonic, since the reconstruction is built by using piecewise polynomials defined by means of an adaption based on the use of the weighted Harmonic mean. The novelty of this work lies in the generalization of the already existing PPH subdivision scheme to the nonuniform case. We define the corresponding subdivision scheme and study some important issues related to subdivision schemes such as convergence, smoothness of the limit function, and preservation of convexity. In order to obtain general results, we consider σ quasi-uniform grids. We also perform some numerical experiments to reinforce the theoretical results.