Maday, Yvon; Nguyen, Ngoc Cuong; Patera, Anthony T.; Pau, S. H. A general multipurpose interpolation procedure: The magic points. (English) Zbl 1184.65020 Commun. Pure Appl. Anal. 8, No. 1, 383-404 (2009). A general multipurpose interpolation method (‘empirical interpolation’) is proposed for constructing a set of basis functions and associated interpolation points (‘magic points’). This iterative method is based on a greedy selection procedure and it does not require involved optimization procedures. The authors demonstrates that the obtained interpolation matrix is invertible and, under certain reasonable conditions, the method provides a convergent interpolant. The efficient implementation and competitiveness of this method is illustrated through several numerical examples in polynomial interpolation over domains with typical or nonstandard geometry, the approximation of parameter-dependent functions, and the approximate solution of parametrized partial differential equations. Reviewer: Aurelian Bejancu (Safat) Cited in 93 Documents MSC: 65D05 Numerical interpolation 41A05 Interpolation in approximation theory Keywords:empirical interpolation; polynomial interpolation; magic points; iterative method; numerical examples × Cite Format Result Cite Review PDF Full Text: DOI