Abstract

We derive an algorithm based on the fast Fourier transform to construct a real symmetric matrix S with eigenvalues ?1 ? ?2 ? ? ? ?n, with eigenvector e = [1,1,..., 1]T belonging to the eigenvalue ?1. We find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix S = ?1E, where E is a symmetric doubly stochastic matrix. © 2003 Elsevier Science Ltd. All rights reserved.