A Test Matrix for an Inverse Eigenvalue Problem
Abstract
We present a real symmetric tridiagonal matrix of order $n$ whose eigenvalues are $\{2k \}_{k=0}^{n1}$ which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, $\{2l + 1 \}_{l=0}^{n2}$. 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 springmass inverse problem incorporating the test matrix is provided.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5890
 Bibcode:
 2014arXiv1402.5890G
 Keywords:

 Mathematics  Numerical Analysis