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

ŞAFAK S.

Bulletin of the Malaysian Mathematical Sciences Society, vol.38, no.2, pp.683-694, 2015 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1007/s40840-014-0043-7
  • Journal Name: Bulletin of the Malaysian Mathematical Sciences Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.683-694
  • Keywords: Inconsistent linear equations, Least squares problem, Penalty function, Generalized inverses, Quadratic programming
  • Dokuz Eylül University Affiliated: Yes

Abstract

© 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.