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

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

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the 12th International Conference on Operational Research KOI2008 / V. Boljunčić, L. Neralić, K. Šorić - Pula : Hrvatsko društvo za operacijska istraživanja (CRORS), 2010, 309-319

Skup
12th International Conference on Operational Research KOI2008

Mjesto i datum
Pula, Hrvatska, 24.09.2008. - 26.09.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Poljoprivreda (agronomija)

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