In 1973 ([2]), I. A. Marusciac defined a class of extremal approximate solution of a linear inconsistent system that contains as particular cases the least square solution and the Tschebychev’s best approximation solution of the system, the two main methods used to obtain an approximate solution of an inconsistent system. The least squares method was applied by M. Fekete and J.M Walsh in 1951 ([1]) in order to obtain an approximate solution of an inconsistent system, whereas the Tschebychev’s best approximation method was used for the same reason by R.L. Remez in 1969 ([3]). In this paper we obtain a first approach in order to show a connection between the ”Pareto minimum solutions” of an inconsistent system and the ”infrasolutions” of this system. First of all we will start with some definitions and known results.
On Pareto Minimum Solutions
PUGLISI, ALFIO
2009-01-01
Abstract
In 1973 ([2]), I. A. Marusciac defined a class of extremal approximate solution of a linear inconsistent system that contains as particular cases the least square solution and the Tschebychev’s best approximation solution of the system, the two main methods used to obtain an approximate solution of an inconsistent system. The least squares method was applied by M. Fekete and J.M Walsh in 1951 ([1]) in order to obtain an approximate solution of an inconsistent system, whereas the Tschebychev’s best approximation method was used for the same reason by R.L. Remez in 1969 ([3]). In this paper we obtain a first approach in order to show a connection between the ”Pareto minimum solutions” of an inconsistent system and the ”infrasolutions” of this system. First of all we will start with some definitions and known results.Pubblicazioni consigliate
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