An inverse eigenvalue problem for pseudo-Jacobi matrices

摘要

In this paper, the theory on direct and inverse spectral problems for Jacobi matrices is revisited in a kind of pseudo-Jacobi matrices J(n,r,β) with a mixed path as its graph in the non-self-adjoint setting. In this context, a sign change in one of the nondiagonal entries of the matrix yields strong perturbations in its spectral properties. The reconstruction of a pseudo-Jacobi matrix from its spectrum and the spectra of two complementary principal matrices is investigated. An algorithm for the reconstruction of matrices from prescribed spectral data is provided and illustrative numerical experiments are performed.