A sparse-sampling approach for the fast computation of matrices:\n application to molecular vibrations

2014/10/17 by Jacob N. Sanders, Sanders, Jacob N., Xavier Andrade +3
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Advanced Fluorescence Microscopy Techniques #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Physics (quant-ph) #Sparse and Compressive Sensing Techniques #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.1410.4848

openalex publication_date 2014/10/17 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28

Abstract

This article presents a new method to compute matrices from numerical\nsimulations based on the ideas of sparse sampling and compressed sensing. The\nmethod is useful for problems where the determination of the entries of a\nmatrix constitutes the computational bottleneck. We apply this new method to an\nimportant problem in computational chemistry: the determination of molecular\nvibrations from electronic structure calculations, where our results show that\nthe overall scaling of the procedure can be improved in some cases. Moreover,\nour method provides a general framework for bootstrapping cheap low-accuracy\ncalculations in order to reduce the required number of expensive high-accuracy\ncalculations, resulting in a significant 3x speed-up in actual calculations.\n

Citations

• Derivative studies in hartree-fock and møller-plesset theories
• Atomic Decomposition by Basis Pursuit
• An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
• Density-functional thermochemistry. III. The role of exact exchange
• Robust principal component analysis?
• rm K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
• Self-Consistent Equations Including Exchange and Correlation Effects

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