ORTHOCUB: integral and differential cubature rules by orthogonal moments

Authors

DOI:

https://doi.org/10.13135/3103-1935/12995

Keywords:

Numerical integration, Numerical differentiation, Quadrature and cubature formulas

Abstract

We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sums corresponding to such integral and differential cubatures are implemented via orthogonal polynomial moments and auxiliary near-minimal algebraic cubature in a bounding box, with no conditioning issue since no matrix inversion or factorization is needed. The whole computational process indeed reduces to moment computation and dense matrix-vector products of relatively small size. The Matlab and Python codes are freely available, to be used as building blocks for integral and differential problems.

Downloads

Published

2026-04-20

How to Cite

Rinaldi, L., Sommariva, A., & Vianello, M. (2026). ORTHOCUB: integral and differential cubature rules by orthogonal moments. Journal of Approximation Software, 3(2). https://doi.org/10.13135/3103-1935/12995

Issue

Vol. 3 No. 2 (2026)

Section

Articles

License

Copyright (c) 2026 Alvise Sommariva, Laura Rinaldi, Marco Vianello

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

JAS only considers unpublished manuscripts.

JAS is committed to electronic open-access publishing since its foundation in 2023 and has chosen to apply the Creative Commons Attribution License (CCAL) CC-BY to all articles.

Under the Creative Commons Attribution License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in JAS, provided that the original authors and source are credited.