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Our method is general, however, and it is applicable to many problems throughout the physical sciences and beyond. The main requirement is an \emph{a priori} guess of a basis in which the matrix to be computed is sparse. The optimal way to achieve this requirement is problem-dependent, but as research into sparsifying transformations continues to develop, we believe our method will enable considerable computational savings in a diverse array of scientific fields.  In fact, an area of interest in compressed sensing is to develop methods that do not directly require the knowledge of a sparsifying basis, but that generate it on-the-fly based on the problem~\cite{10.1109/TSP.2006.881199}. problem~\cite{Aharon_2006}.  CITE!!!!