A new method for searching an L1 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 Ax = b, A is an element of 1R(mXn),b is an element of R-m, (m >> ni), in the sense of least absolute deviations min(x is an element of R '') parallel to b-Ax parallel to(1) The method is based upon the fact that, if A is a matrix with full column rank, then there exists x* is an element of 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.