A Douglas-Rachford splitting algorithm with closed-form projection computes substantially sparser symmetric generalized inverses than the Moore-Penrose pseudoinverse for sparse symmetric matrices.
Good and fast row-sparse ah-symmetric reflexive generalized inverses,
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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.