A Finite Step Algorithm for Determining the “Strict” Chebyshev Solution to $Ax=b$

Abstract

This paper develops a finite step algorithm for determining the “strict” Chebyshev solution to an overdetermined system of linear equations $Ax = b$, where A is an $m \times n$ matrix of rank $n < m$. The construction of the strict Chebyshev solution is based on a new way of constructively defining the strict solution, which is shown to be equivalent to the construction based on knowing all the possible Chebyshev solutions. A discussion of the computational problems encountered in this algorithm is given, along with the solutions to some examples.