A general multipurpose interpolation procedure: The magic points (Q2518242)

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.