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Abstract
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization of the polynomial interpolation theory developed for a node set known as Padua points. With appropriately defined polynomial spaces, we will show that the node points of nondegenerate Lissajous curves allow unique interpolation and can be used for quadrature rules in the bivariate setting. An explicit formula for the Lagrange polynomials allows to compute the interpolating polynomial with a simple algorithmic scheme. Compared to the already established schemes of the Padua and Xu points, the numerical results for the proposed scheme show similar approximation errors and a similar growth of the Lebesgue constant.
Original language  English 

Journal  Numerische Mathematik 
Volume  133 
Issue number  4 
Pages (fromto)  685705 
Number of pages  21 
ISSN  0029599X 
DOIs  
Publication status  Published  01.08.2016 
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Dive into the research topics of 'Bivariate Lagrange interpolation at the node points of nondegenerate Lissajous curves'. Together they form a unique fingerprint.Projects
 1 Finished

Development, analysis and application of mathematical methods for Magnetic Particle Imaging (MathMPI)
Erb, W.
01.08.14 → 31.12.16
Project: DFG Projects › DFG Individual Projects