Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Mohammad Adm

A real matrix is called sign regular if all its nonzero minors of the same order have identical sign. Such matrices arise in a remarkable variety of ways in mathematics and many areas of its applications such as differential and integral equations, function theory, approximation theory, reductive Lie groups, computer aided geometric design, mathematical finance, and mechanics.

A great deal of papers is devoted to the problem of determining whether a given n-by-n matrix is in a given subclass ofsign regular matrices. One could calculate each of its minors, but that would involve evaluating about $4^n/\sqrt(n\pi)$ subdeterminants for a given n-by-n matrix! The question arises whether there is an efficient algorithm to test membership of a given matrix in a certain subclass of sign regular matrices. In this talk, we present the so-called Cauchon Algorithm and necessary and sufficient conditions for using it to check a given matrix to be in some subclasses of sign regular matrices.