Orthant-monotonic norms and overdetermined linear systems

[摘要] In the paper the properties of parallel to . parallel to-approximate solutions 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, me consider the relation between the sets of the weighted approximate solutions for the orthant-monotonic norms satisfying some additional conditions. (C) 1997 Academic Press.

[发布日期] 1997-02-01