The Best Approximate Solution of the Inconsistent Linear System via a Quadratic Penalty Function

被引：1

作者：

Safak, S. ^{[1
]}

机构：

[1] Dokuz Eylul Univ, Fac Engn, Div Math, TR-35160 Izmir, Turkey

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2015年 / 38卷 / 02期

关键词：

Inconsistent linear equations; Least squares problem; Penalty function; Generalized inverses; Quadratic programming; TIKHONOV REGULARIZATION; ITERATIVE METHODS; MINIMUM;

D O I：

10.1007/s40840-014-0043-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the inconsistent linear system of equations in 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.

引用

页码：683 / 694

页数：12

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