Abstract
The problem is considered of generating approximate quantum-mechanical wavefunctions that have as many as possible coefficients held exactly to zero for a given desired accuracy. Two approaches are adopted. In the first, perturbation theory within the Davidson diagonalisation algorithm is used to mask off small coefficients in the wavefunction against a predefined target energy threshold. Second, sparsity is introduced by penalty-function optimisation, with a norm-based compressive-sampling penalty function that decreases with increasing sparsity. The first approach is found to be robust and reliable, whereas the second does not succeed in keeping the wavefunction sparse.
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