Dynamic inverse problem for complex Jacobi matrices

TL;DR

This paper investigates the inverse problem for a discrete-time dynamical system modeled by a semi-infinite complex Jacobi matrix, proposing methods to recover system coefficients from dynamic response data.

Contribution

It introduces two approaches for reconstructing coefficients from dynamic response operators and characterizes the inverse data for complex Jacobi matrices.

Findings

Proposed two methods for coefficient recovery.

Provided a characterization of dynamic inverse data.

Enhanced understanding of inverse problems for complex Jacobi matrices.

Abstract

We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a question on the characterization of dynamic inverse data.