A direct method for sparse least squares problems with lower and upper bounds

SummaryA direct method is developed for solving linear least squares problems $$\mathop {\min \left\| {Ax - b} \right\|_2 }\limits_x $$ , whereA is large and sparse and the solution is subject to lower and upper boundsl≦x≦u. The problem is initially transformed to upper triangular form by a sparseQR-factorization. An active set algorithm is then used. The key step is the stable updating of theR-factor associated with the columns ofA corresponding to the free variables, when theQ-factor is not available. For this a new method is developed, which uses the semi-normal equations and iterative refinement.

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