This talk presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes the computational bottleneck, as is the case when computing electronic structure properties of large systems. In particular, we apply this new method to the determination of molecular vibrations from electronic structure calculations, where our results show that the overall scaling of the procedure can be improved in some cases. Moreover, our method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations, resulting in a significant 3x speed-up in actual calculations. We believe this method, which can potentially be combined with other optimizations, can help to enable the fast calculation of molecular vibrations for large systems.

Compressed sensing for the fast computation of matrices: Application to molecular vibrations

250th National Meeting (2015)

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