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This paper introduces a new framework for constructing the Discrete EmpiricalInterpolation Method DEIM projection operator. The interpolation node selectionprocedure is formulated using the QR factorization with column pivoting, and itenjoys a sharper error bound for the DEIM projection error. Furthermore, for asubspace $\mathcal{U}$ given as the range of an orthonormal $U$, the DEIMprojection does not change if $U$ is replaced by $U \Omega$ with arbitraryunitary matrix $\Omega$. In a large-scale setting, the new approach allowsmodifications that use only randomly sampled rows of $U$, but with thepotential of producing good approximations with corresponding probabilisticerror bounds. Another salient feature of the new framework is that robust andefficient software implementation is easily developed, based on readilyavailable high performance linear algebra packages.

A New Selection Operator for the Discrete Empirical Interpolation Method -- improved a priori error bound and extensions