PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2007 | 5 | 2 | 373-385
Tytuł artykułu

On stable least squares solution to the system of linear inequalities

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable and degenerate problems primarily.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
2
Strony
373-385
Opis fizyczny
Daty
wydano
2007-06-01
online
2007-01-26
Twórcy
autor
Bibliografia
  • [1] C. Lawson and R. Hanson: Solving Least Squares Problems, Prentice-Hall, New-Jersey, 1974.
  • [2] E. Übi: “Exact and Stable Least Squares Solution to the Linear Programming Problem”, Centr. Eur. J. Math., Vol. 3(2), (2005), pp. 228–241. http://dx.doi.org/10.2478/BF02479198
  • [3] Fan Ky: “On Systems of Linear Inequalities”, In: H. Kuhn and W. Tucker (Eds.): Linear Inequalities and Related Systems, Priceton, 1956.
  • [4] E. Übi: “Finding Non-negative Solution of Overdetermined or Underdetermined System of Linear Equations by Method of Least Squares”, Transactions of Tallinn TU, Vol. 738, (1994), pp. 61–68.
  • [5] C. Papadimitriou and K. Steiglitz: Combinatorial Optimization:Algorithms and Complexity, Prentice-Hall, New-Jersey, 1982.
  • [6] L. Khachiyan: “A Polynomial Algorihm in linear programming”, Soviet Mathematics Doklady, Vol. 20, (1979), pp. 191–194.
  • [7] L. Khachiyan: “Fourier-Motzkin Elimination Method”, Encyklopedia of Optimization, Vol. 2, (2001), pp. 155–159.
  • [8] G. Danzig: Linear Programming and Extensions, Princeton University Press, 1963.
  • [9] S. Chernikov: Lineare Ungleichungen, Deutscher Verlag der Wissenschaften, Berlin, 1971.
  • [10] D. Gale: The Theory of Linear Economic Models, McGgraw-HILL Book Company, 1960.
  • [11] A. Björck: “Generalized and Sparse Least Squares Problems”, NATO ASI Series C, Vol. 434, (1994), pp. 37–80.
  • [12] M. Hath: “Some Extensions of an algorithm for Sparse Linear Least Squares Problems”, SIAM J.Sci. Statist. Comput., Vol. 3, (1982), pp. 223–237. http://dx.doi.org/10.1137/0903014
  • [13] L. Bregman: “The Method of Successive Projecton for Finding The Common Point of Convex Set”, Soviet. Math. Dokl., Vol. 6, (1969), pp. 688–692.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0003-7
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.