Remark on algorithm 587

ABSTRACT

The subroutine WNNLS of Algorithm 587 has exposed some shortcomings, especially in solving rank-deficient problems. They may lead to fatal errors and (or) false results. Five improvements are proposed. The effect of the changes is tested on four rank-deficient test problems. It is emphasized that the WNNLS still remains vulnerable to bad scaling of the problem.

REFERENCES

• 1: Richard J Hanson, Linear least squares with bounds and liner constraints, SIAM Journal on Scientific and Statistical Computing, v.7 n.3, p.826-834, July 1986 [doi>10.1137/0907055]
• 2: Richard J. Hanson , Karen H. Haskell, Algorithm 587: Two Algorithms for the Linearly Constrained Least Squares Problem, ACM Transactions on Mathematical Software (TOMS), v.8 n.3, p.323-333, Sept. 1982 [doi>10.1145/356004.356010]
• 3: HASKELL, K. H., AND HANSON, R.J. An algorithm for linear least squares problems with equality and nonnegativity constraints. Math. Program 21 (1981), 98-118.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Constrained optimization

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Least squares approximation
      G.1.6 Optimization
          Subjects: Least squares methods

General Terms:
Algorithms, Theory