A direct method for sparse least squares problems with lower and upper bounds. (English) Zbl 0659.65039

The least squares problem \(\| Ax-b\|_ 2\to Min\). (the solution of which being subject to the additional restriction \(1\leq x\leq u)\) is solved by QR-factorization (using SPARSEPAK), followed by a stable updating procedure for R. The main point is that the updating avoids fill-in and uses the fixed data structure of the factor R. Comparing numerical tests between the new method and the algorithm NNLS of C. L. Lawson and R. J. Hanson (Solving least squares problems. (1974; M.R. 51.2270)] show remarkable savings both in CPU-time and in storage requirements.
Reviewer: G.Maeß


65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F05 Direct numerical methods for linear systems and matrix inversion


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