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The discrete empirical interpolation method (DEIM) may be used as an indexselection strategy for formulating a CUR factorization. A notable drawback ofthe original DEIM algorithm is that the number of column or row indices thatcan be selected is limited to the number of input singular vectors. We proposea new variant of DEIM, which we call L-DEIM, a combination of the strength ofdeterministic leverage scores and DEIM. This method allows for the selection ofa number of indices greater than the number of available singular vectors.Since DEIM requires singular vectors as input matrices, L-DEIM is particularlyattractive for example in big data problems when computing a rank-$k$-SVDapproximation is expensive even for moderately small $k$ since it uses alower-rank SVD approximation instead of the full rank-$k$ SVD. We empiricallydemonstrate the performance of L-DEIM, which despite its efficiency, mayachieve comparable results to the original DEIM and even better approximationsthan some state-of-the-art methods.

A hybrid DEIM and leverage scores based method for CUR index selection