A Douglas-Rachford splitting algorithm with closed-form projection computes substantially sparser symmetric generalized inverses than the Moore-Penrose pseudoinverse for sparse symmetric matrices.
On computing sparse universal solvers for key problems in statistics
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abstract
We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal least-squares solvers, and simultaneous universal minimum-norm/least-squares solvers. For all of these, we present and compare several new alternative linear-programming formulations and very effective proximal-point algorithms. Overall, we found that our new Douglas-Rachford splitting algorithms for these problems performed best.
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2026 1verdicts
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Sparse symmetric generalized inverses for sparse symmetric matrices
A Douglas-Rachford splitting algorithm with closed-form projection computes substantially sparser symmetric generalized inverses than the Moore-Penrose pseudoinverse for sparse symmetric matrices.