Volume 51, pp. 363-386, 2019.

On the construction of real non-selfadjoint tridiagonal matrices with prescribed three spectra

Wei-Ru Xu, Natália Bebiano, and Guo-Liang Chen


Non-selfadjoint tridiagonal matrices play a role in the discretization and truncation of the Schrödinger equation in some extensions of quantum mechanics, a research field particularly active in the last two decades. In this article, we consider an inverse eigenvalue problem that consists of the reconstruction of such a real non-selfadjoint matrix from its prescribed eigenvalues and those of two complementary principal submatrices. Necessary and sufficient conditions under which the problem has a solution are presented, and uniqueness is discussed. The reconstruction is performed by using a modified unsymmetric Lanczos algorithm, designed to solve the proposed inverse eigenvalue problem. Some illustrative numerical examples are given to test the efficiency and feasibility of our reconstruction algorithm.

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Key words

inverse eigenvalue problem, non-selfadjoint tridiagonal matrix, modified unsymmetric Lanczos algorithm, spectral data

AMS subject classifications

65F18, 65F15, 15A18, 15A29

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