Abstract

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