Abstract
The Chebyshev solution of an overdetermined system of linear equation is considered when linear constraints on the solution are present. Constraints considered are constraints on the given matrix of coefficients plus general linear constraints. No assumption on the matrix of coefficients, such as the Haar condition, is made; thus the most general discrete linear problem is considered. Use is made of the concept of H-sets to give characterization theorems. An ascent exchange algorithm is given with numerical examples. Convergence of the algorithm when the problem has a solution is proven, and a computable condition is given for the case when the constraints make the problem infeasible.
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