Krystyna Zietak
"Orthant-Monotonic Norms and Overdetermined Linear Systems"

In the paper the properties of approximate solutions (with respect to 
some norms) of real overdetermined linear systems Ax=b are investigated. 
We characterize the norms for which the approximate solutions are in 
the convex hull of the basic solutions of Ax=b. For this purpose we prove 
some properties of the orthant-monotonic norms. We derive an explicit formula 
which expresses the approximate solutions of Ax=b, with respect to some 
norms, as convex combinations of the basic solutions for an n+1 by n real 
matrix A of rank n. Moreover, we consider the relation between the sets of 
the approximate weigthed solutions for the orthant-monotonic norms satisfying 
additional conditions.

Keywords and phrases: overdetermined linear system,  weighted solutions,
                      convex hull of basic solutions, orthant-monotonic norms,
                      isotone functions