Geodesic
On the computer-algebra implementation of the least-squares method on the nonnegative orthant
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 23-29 
Kh. D. Ikramov; M. Matin far. On the computer-algebra implementation of the least-squares method on the nonnegative orthant. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 23-29. http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a2/
@article{ZNSL_2004_309_a2,
     author = {Kh. D. Ikramov and M. Matin far},
     title = {On the computer-algebra implementation of the least-squares method on the nonnegative orthant},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {23--29},
     year = {2004},
     volume = {309},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a2/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
AU  - M. Matin far
TI  - On the computer-algebra implementation of the least-squares method on the nonnegative orthant
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 23
EP  - 29
VL  - 309
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a2/
LA  - ru
ID  - ZNSL_2004_309_a2
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%A M. Matin far
%T On the computer-algebra implementation of the least-squares method on the nonnegative orthant
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 23-29
%V 309
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a2/
%G ru
%F ZNSL_2004_309_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Maple procedures for solving the so-called NNLS (Nonnegative Least Squares) problem are described. The NNLS problem is to minimize $$ ||Ex-f||_2 $$ subject to $$ x\geqslant0. $$ The solution of an NNLS problem is the crucial step OF the conventional algorithm for solving linear least-squares problems with linear inequality constraints.

[1] Kh. D. Ikramov, M. Matin far, “O kompyuterno-algebraicheskikh protsedurakh dlya psevdoobrascheniya matrits”, ZhVM i MF, 43 (2003), 163–168 | MR | Zbl

[2] Kh. D. Ikramov, M. Matin far, “Odnorangovye modifikatsii i pereschet psevdoobratnykh matrits”, Vestnik Mosk. un-ta. Seriya 15. Vychisl. matem. kibernet., 4 (2002), 12–17 | MR | Zbl

[3] Kh. D. Ikramov, M. Matin far, “Pereschet normalnykh psevdoreshenii pri odnorangovykh modifikatsiyakh matritsy”, ZhVM i MF, 43 (2003), 493–505 | MR | Zbl

[4] Kh. D. Ikramov, M. Matin far, “O kompyuterno-algebraicheskikh protsedurakh dlya lineinoi zadachi naimenshikh kvadratov s lineinymi svyazyami”, ZhVM i MF, 44 (2004), 206–212 | MR | Zbl

[5] C. L. Lawson, R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, 1974 | MR