The smallest eigenvalue of large Hankel matrices generated by a singularly perturbed Laguerre weight

Abstract

An asymptotic expression of the orthonormal polynomials P N (z) as N → ∞, associated with the singularly perturbed Laguerre weight w α (x; t) = x α e −x− t x , x ∈ [0, ∞), α > −1, t ≥ 0 is derived. Based on this, we establish the asymptotic behavior of the smallest eigenvalue, λ N , of the Hankel matrix generated by the weight w α (x; t).

An inexact Krylov subspace method for large generalized Hankel eigenproblems

“…A fast eigenvalue algorithm for Hankel matrices was proposed [3] based on the Lanczos-type tridiagonalization and QR-type diagonalization methods. Some studies [4][5][6][7] have focused specifically on the smallest eigenvalue of large scale Hankel matrices. The sensitivity of the nonlinear application [2] mapping the vector of Hankel entries to its generalized eigenvalues was studied.…”