Inverse problems for periodic generalized Jacobi matrices

Marchenko-Ostrovski mappings for periodic Jacobi matrices

We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on the quasimomentum domain . Furthermore, we obtain a priori two-sided estimates for vertical slits in terms of Jacoby matrices.

On an inverse eigenproblem for Jacobi matrices

Recently Xu 13] proposed a new algorithm for computing a Jacobi matrix of order 2n with a given n n leading principal submatrix and with 2n prescribed eigenvalues that satisfy certain conditions. We compare this algorithm to a scheme proposed by Boley and Golub 2], and discuss a generalization that allows the conditions on the prescribed eigenvalues to be relaxed.

Generalized inverse eigenvalue problems for symmetric arrow-head matrices

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices Ã, B̃ ∈ Rn×n, find (Â, B̂) ∈ SE such that ‖Â...

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Two modified Jacobi methods for M-matrices