Some Numerical Aspects of the Cauchon

Abstract

A real matrix is called totally nonnegative or totally positive if all minors are nonnegative or positive, respectively. In this thesis, we derive the condensed form of the Restoration Algorithm which is a new result and it is the inverse of the condensed form of the Cauchon Algorithm where the latter provides an efficient tool to check a given matrix to be totally nonnegative or totally positive. In this thesis we perform some elementary operations on a nonsingular totally nonnegative matrix and apply the condensed form of the Cauchon Algorithm on it, we determine how the entries of this matrix are changing after performing the elementary operations. Also, we present a new algorithm for computing the eigenvalues of a nonsingular totally nonnegative matrices with high accuracy using the results obtained in this thesis.