The Gel'fand-Levitan-Krein method and the globally convergent method for experimental data

TL;DR

This paper compares the numerical performance of the classical Gel'fand-Levitan-Krein method and a recently developed globally convergent method for solving coefficient inverse problems using both simulated and experimental data.

Contribution

It provides a comparative analysis of two different numerical methods for inverse problems, highlighting the effectiveness of the globally convergent approach.

Findings

The globally convergent method performs well on experimental data.

Comparison shows advantages of the globally convergent method over classical approaches.

Numerical results demonstrate the applicability of both methods to real-world data.

Abstract

Comparison of numerical performances of two methods for coefficient inverse problems is described. The first one is the classical Gel'fand-Levitan-Krein equation method, and the second one is the recently developed approximately globally convergent numerical method. This comparison is performed for both computationally simulated and experimental data.