Truncations of a class of pseudo-Hermitian operators

2015/03/14 by Maxim Derevyagin, Derevyagin, Maxim, Luca Perotti +3
Computer Science · Mathematics · Physics and Astronomy · #47B36 #47B50 #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1503.04314

openalex publication_date 2015/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the class of non-Hermitian operators represented by infinite tridiagonal matrices, selfadjoint in an indefinite inner product space with one negative square. We approximate them with their finite truncations. Both infinite and truncated matrices have eigenvalues of nonpositive type: either a single one on the real axis or a couple of complex conjugate ones. As a tool to evaluate the reliability of the use of truncations in numerical simulations, we give bounds for the rate of convergence of their eigenvalues of nonpositive type. Numerical examples illustrate our results.

Citations

• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications

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