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A new method for searching an $L_1$ solution of an overdetermined system of linear equations and applications (CROSBI ID 563437)

Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija

Kušec, Goran ; Kuzmanović, Ivana ; Sabo, Kristian ; Scitovski, Rudolf A new method for searching an $L_1$ solution of an overdetermined system of linear equations and applications // Proceedings of the 12th International Conference on Operational Research KOI2008 / V. Boljunčić, L. Neralić, K. Šorić (ur.). Pula: Hrvatsko društvo za operacijska istraživanja (CRORS), 2010. str. 309-319

Podaci o odgovornosti

Kušec, Goran ; Kuzmanović, Ivana ; Sabo, Kristian ; Scitovski, Rudolf

engleski

A new method for searching an $L_1$ solution of an overdetermined system of linear equations and applications

In this paper we consider a new method for searching a solution of an overdetermined system of linear equations $\mathbf{; ; Ax}; ; =\mathbf{; ; b}; ; $, $\mathbf{; ; A}; ; \in \mathbb{; ; R}; ; ^{; ; m\times n}; ; , \, \mathbf{; ; b}; ; \in\mathbb{; ; R}; ; ^m$, $(m\gg n)$, in the sense of least absolute deviations \ [\min_{; ; \mathbf{; ; x}; ; \in\mathbb{; ; R}; ; ^n}; ; \|\mathb f{; ; b}; ; -\mathbf{; ; Ax}; ; \|_1.\] The method is based upon the fact that, if $\mathbf{; ; A}; ; $ is a matrix with full column rank, then there exists $\mathbf{; ; x^*}; ; \in\mathbb{; ; R}; ; ^n$, such that it satisfies at least $n$ equations of the system. In operational research literature this problem is most frequently considered as the problem of estimating hyperplane parameters. Such problems appear very often in various fields of applied research in cases if among the data a significant number of outliers appears. We will show the application of this method to the problem of estimating the percentage of muscle tissue in pigs, based upon real measurement data obtained on $145$ pig carcasses from the dissection trial in Croatia.

mathematical model ; least absolute deviations ; selection ; estimation of the percentage of muscle tissue

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Podaci o prilogu

309-319.

2010.

objavljeno

Podaci o matičnoj publikaciji

Proceedings of the 12th International Conference on Operational Research KOI2008

V. Boljunčić, L. Neralić, K. Šorić

Pula: Hrvatsko društvo za operacijska istraživanja (CRORS)

Podaci o skupu

Nepoznat skup

predavanje

29.02.1904-29.02.2096

Povezanost rada

Matematika, Poljoprivreda (agronomija)