A Test Matrix for an Inverse Eigenvalue Problem

Abstract

We present a real symmetric tridiagonal matrix of order n whose eigenvalues are {2k}k=0n-1 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l+1}l=0n-2. The matrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided.