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Computer-Algebra Implementation of the Least-Squares Method on the Nonnegative Orthant

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Abstract

Maple procedures for solving the so-called NNLS (Nonnegative Least Squares) problem are described. The NNLS problem is to minimize

$$\left\| {Ex - f} \right\|_2$$

subject to

$$x \geqslant 0.$$

The solution of an NNLS problem is the crucial step of the conventional algorithm for solving linear least-squares problems with linear inequality constraints. Bibliography: 5 titles.

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REFERENCES

  1. Kh. D. Ikramov and M. Matin far, “Computer-algebra procedures for matrix pseudoinversion,” Zh. Vychisl. Mat. Mat. Fiz., 43, 163–168 (2003).

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  2. Kh. D. Ikramov and M. Matin far, “Rank-one modifications and updating pseudoinverse matrices,” Vestn. Mosk. Gos. Univ. Ser. 15 Vychisl. Mat. Kibern., No. 4, 12–17 (2003).

  3. Kh. D. Ikramov and M. Matin far, “Updating the minimum-norm least-squares solution under rank-one modifications of a matrix,” Zh. Vychisl. Mat. Mat. Fiz., 43, 493–505 (2003).

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  4. Kh. D. Ikramov and M. Matin far, “On computer-algebra procedures for linear least-squares problems with linear equality constraints,” Zh. Vychisl. Mat. Mat. Fiz., 44, 206–212 (2004).

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  5. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs (1974).

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Authors and Affiliations

  1. Moscow State University, Russia

    Kh. D. Ikramov & M. Matin far

Authors
  1. Kh. D. Ikramov
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  2. M. Matin far
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__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 23–29.

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Ikramov, K.D., Matin far, M. Computer-Algebra Implementation of the Least-Squares Method on the Nonnegative Orthant. J Math Sci 132, 156–159 (2006). https://doi.org/10.1007/s10958-005-0485-4

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  • DOI: https://doi.org/10.1007/s10958-005-0485-4

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