An iterated quasi-interpolation approach for derivative approximation
Numerical Algorithms, ISSN: 1572-9265, Vol: 85, Issue: 1, Page: 255-276
2020
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Article Description
Given discrete function values sampled at uniform centers, the iterated quasi-interpolation approach for approximating the m th derivative consists of two steps. The first step adopts m successive applications of the operator DQ (the quasi-interpolation operator Q first, and then the differentiation operator D) to get approximated values of the m th derivative at uniform centers. Then, by one further application of the quasi-interpolation operator Q to corresponding approximated derivative values gives the final approximation of the m th derivative. The most salient feature of the approach is that it approximates all derivatives with the same convergence rate. In addition, it is valid for a general multivariate function, compared with the existing iterated interpolation approaches that are only valid for periodic functions, so far. Numerical examples of approximating high-order derivatives using both the iterated and direct approach based on B-spline quasi-interpolation and multiquadric quasi-interpolation are presented at the end of the paper, which demonstrate that the iterated quasi-interpolation approach provides higher approximation orders than the corresponding direct approach.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85081574710&origin=inward; http://dx.doi.org/10.1007/s11075-019-00812-9; http://link.springer.com/10.1007/s11075-019-00812-9; http://link.springer.com/content/pdf/10.1007/s11075-019-00812-9.pdf; http://link.springer.com/article/10.1007/s11075-019-00812-9/fulltext.html; https://dx.doi.org/10.1007/s11075-019-00812-9; https://link.springer.com/article/10.1007/s11075-019-00812-9
Springer Science and Business Media LLC
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