Hermite subdivision schemes, exponential polynomial generation, and annihilators

We consider the question when the so--called spectral condition} for Hermite subdivision schemes extends to spaces generated by polynomials and exponential functions. The main tool are convolution operators that annihilate the space in question which apparently is a general concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of the subdivision operator

On Multi-Rule and Probability-Dependant Adaptations of Conway’s Game of Life and Their Character

Source at https://www.oldcitypublishing.com/journals/jca-home/jca-issue-contents/jca-volume-16-number-3-4-2022/.We introduce some novel adaptations of Life-Like Automata. We focus mainly on some modifications of the original rules where the evolution of the system is depending from the step and the zone of the grid. We study also the properties of some novel non-deterministic adaptations

Single-precision arithmetic in ECHAM radiation reduces runtime and energy consumption

We converted the radiation part of the atmospheric model ECHAM to a single-precision arithmetic. We analyzed different conversion strategies and finally used a step-by-step change in all modules, subroutines and functions. We found out that a small code portion still requires higher-precision arithmetic. We generated code that can be easily changed from double to single precision and vice versa, basically using a simple switch in one module. We compared the output of the single-precision version in the coarse resolution with observational data and with the original double-precision code. The results of both versions are comparable. We extensively tested different parallelization options with respect to the possible runtime reduction, at both coarse and low resolution. The single-precision radiation itself was accelerated by about 40 %, whereas the runtime reduction for the whole ECHAM model using the converted radiation achieved 18 % in the best configuration. We further measured the energy consumption, which could also be reduced

Beyond B-splines: Exponential pseudo-splines and subdivision schemes reproducing exponential polynomials

The main goal of this paper is to present some generalizations of polynomial B-splines, which include exponential B-splines and the larger family of exponential pseudo-splines. We especially focus on their connections to subdivision schemes. In addition, we generalize a well-known result on the approximation order of exponential pseudo-splines, providing conditions to establish the approximation order of nonstationary subdivision schemes reproducing spaces of exponential polynomial function

Full rank interpolatory subdivision schemes: Kronecker, filters and multiresolution

AbstractIn this extension of earlier work, we point out several ways how a multiresolution analysis can be derived from a finitely supported interpolatory matrix mask which has a positive definite symbol on the unit circle except at −1. A major tool in this investigation will be subdivision schemes that are obtained by using convolution or correlation operations based on replacing the usual matrix multiplications by Kronecker products