A survey on bivariate Lagrange interpolation on Lissajous nodes. (English) Zbl 1370.41006

Erb, Wolfgang; Kaethner, Christian; Dencker, Peter; Ahlborg, Mandy

Dolomites Res. Notes Approx. 8, Spec. Iss., 23-36 (2015).

Summary: This article is a survey on recent research on bivariate polynomial interpolation on the node points of Lissajous curves. The resulting theory is a generalization of the generating curve approach developed for Lagrange interpolation on the Padua points. After classifying the different types of Lissajous curves, we give a short overview on interpolation and quadrature rules defined on the node points of the Lissajous curves. Further, we summarize some convergence results and show how the interpolating polynomials can be computed efficiently. Finally, the developed theory is applied to a practical problem from a medical imaging modality called Magnetic Particle Imaging.

MSC:

41A05	Interpolation in approximation theory
94A08	Image processing (compression, reconstruction, etc.) in information and communication theory

Software:

LS2Ditp