An inverse spectral problem for a damped wave operator

2020/08/11 by Gang Bao, Xiang Xu, Bao, Gang +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.04523

openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting a sequence of trace formulas, which are deduced by a recursive formula, bridging geometrical and spectrum information explicitly in terms of Fredholm integral equations. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

Citations

• One-parameter semigroups for linear evolution equations
• Inversion of trace formulas for a Sturm-Liouville operator

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