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arXiv · 2401.17540

Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses

Gabriel Ponte·Marcia Fampa·Jon Lee·Luze Xu
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Abstract

We present several algorithms aimed at constructing sparse and structured sparse (row-sparse) generalized inverses, with application to the efficient computation of least-squares solutions, for inconsistent systems of linear equations, in the setting of multiple right-hand sides and a rank-deficient constraint matrix. Leveraging our earlier formulations to minimize the 1- and 2,1- norms of generalized inverses that satisfy important properties of the Moore-Penrose pseudoinverse, we develop efficient and scalable ADMM algorithms to address these norm-minimization problems and to limit the number of nonzero rows in the solution. We establish a 2,1-norm approximation result for a local-search procedure that was originally designed for 1-norm minimization, and we compare the ADMM algorithms with the local-search procedure and with general-purpose optimization solvers.

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Gabriel Ponte, Marcia Fampa, Jon Lee, Luze Xu. 2024-01-31. Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses. https://arxiv.org/abs/2401.17540

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