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

Abstract

A necessary and sufficient condition for an n-tuple of real numbers ( λ 1, λ 2, …, λ n ) to be the spectrum of an oscillatory matrix is that λ 1 > λ 2 > … > λ n > 0. Some methods of constructing a positive symmetric oscillatory matrix with spectrum σ = λ 1, λ 2, …, λ 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.