Boundary control and Gel'fand–Levitan–Krein methods in inverse acoustic problem

Abstract

In this paper we study the inverse problem for the acoustic equation. The boundary control method (BC-method) and Gel'fand—Levitan—Krein method (GLK-method) are investigated and compared. In Section 1 inverse acoustic problem is formulated. In Section 2 we consider the scheme of BC-method. In Section 3 the multidimensional analog of Gel'fand—Levitan—Krein equation is obtained for inverse acoustic problem. In Section 4 we investigate discrete analogs of main relations of both methods. In Section 5 we consider the numerical results.