The best approximate solution of the inconsistent linear system via a quadratic penalty function

ŞAFAK S.

Bulletin of the Malaysian Mathematical Sciences Society, cilt.38, sa.2, ss.683-694, 2015 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s40840-014-0043-7
  • Dergi Adı: Bulletin of the Malaysian Mathematical Sciences Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.683-694
  • Anahtar Kelimeler: Inconsistent linear equations, Least squares problem, Penalty function, Generalized inverses, Quadratic programming
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2014.In this paper, the inconsistent linear system of m equations in n unknowns is formulated as a quadratic programming problem, and the best approximate solution with the minimum norm for the inconsistent system of the linear equations is investigated using the optimality conditions of the quadratic penalty function (QPF). In addition, several algebraic characterizations of the equivalent cases of the QPF are given using the orthogonal decompositions of the coefficient matrices obtained from optimality conditions, and analytic results we obtained are satisfied with numerical examples.