A note on the construction of a positive oscillatory matrix with a prescribed spectrum

A necessary and sufficient condition for an n-tuple of real numbers (lambda (1),lambda (2),...,lambda (n)) to be the spectrum of an oscillatory matrix is that lambda (1) > lambda (2) > ... > lambda (n) > 0. Some methods of constructing a positive symmetric oscillatory matrix with s pectrum sigma = {lambda (1),lambda (2),...,lambda (n)} are suggested for th eorems concerning oscillatory matrices. In this work, we present a new proc edure of constructing such a matrix which is numerically stable and appears to be less expensive. (C) 2001 Elsevier Science Ltd. All rights reserved.