Three Cuts for Accelerated Interval Propagation

This paper addresses the problem of nonlinear multivariate root nding. In an earlier paper we describe a system called Newton which nds roots of systems of nonlinear equations using re nements of interval methods. The re nements are inspired by AI constraint propagation techniques. Newton is competitive with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three \cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only brie y discussed here. Copyright c Massachusetts Institute of Technology, 1995 This report describes research done at the Arti cial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's arti cial intelligence research was provided in part by the Advanced Research Projects Agency of the Department of Defense under O ce of Naval Research contract N00014-91-J-4038. This research was also partly supported by the O ce of Naval Research under grant N00014-91-J-4052 ARPA order 8225, the National Science Foundation under grant numbers CCR-9357704, an NSF National Young Investigator Award.