2021/05/27 by Enno Diekema, Diekema, Enno
Engineering · Mathematics · #Advanced Measurement and Metrology Techniques #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Control Systems and Identification #FOS: Mathematics #math.CA
paper · pdf · doi:10.48550/arxiv.2105.13019
arxiv created 2021/05/27 · openalex publication_date 2021/05/27 · arxiv updated 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The orthogonal derivative is defined as a limit of an integral whose kernel contains an orthogonal polynomial with its measure. When in practice no limit is taken, it means that the accuracy of the derivative depends on the second derivative of the given function. Liptaj shows that it is possible to define a kernel in such a way that the accuracy depends on a higher derivative at your own choice. The accuracy is therefore much greater than with the orthogonal derivative. However Diekema and Koornwinder find a similar extension starting directly from of the orthogonal derivative. The new kernel is not orthogonal for order greater then one. The transfer function for this new derivative is given.