## Version 1.0.0

June 2020

Recent Changes

HSL_MA85 uses a direct method to solve large-scale diagonally-weighted linear least squares problems. Given an $$m \times n$$ ($$m \ge n$$) matrix $${A} = \{ a_{ij} \}$$, an $$m \times m$$ diagonal matrix of weights $$W$$, and an $$m-$$vector $$b$$, HSL_MA85 solves either the least squares problem $\label{eq:ls} \min_x \| W(Ax - b) \|^2_2 ,$ or the regularized least squares problem $\label{eq:ls_reg} \min_x \| W(Ax - b) \|^2_2 + \alpha\|x\|^2_2,$ where $$\alpha > 0$$ is a regularization parameter chosen by the user. The matrix $$A$$ may contain one or more rows that are to be treated as dense but must otherwise be sparse. Rows of $$A$$ that lead to a large amount of fill in the normal matrix should be treated as dense (they may contain fewer than $$n$$ non zero entries but generally have more non zeroes than the other rows of $$A$$). The package offers the option of (i) a Cholesky-based approach or (ii) an approach that uses a symmetric indefinite solver applied to the (regularized) augmented system.