The purpose of this paper is to describe various results which pertain to a class of variational problems in which two or more error criteria are to be controlled simultaneously in some optimal fashion. This type of problem has wide application In optimal control, statistical estimation and approximation theory. We make no pretense that our treatment is exhaustive either in the applications we cover or in the analysis we use, Rather, we wish to point out some general properties of these problems that are useful, survey some interesting examples which arise in applications, and give an analysis of certain classes of these variational problems where total positivity plays a central sole.
By: Charles A. Micchelli, Allan Pinkus
Published in: RC18699 in 1993
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .