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 (λ1, λ2, …, λn) to be the spectrum of an oscillatory matrix is that λ1 > λ2 > … > λn > 0. Some methods of constructing a positive symmetric oscillatory matrix with spectrum σ = λ1, λ2, …, λn 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.