Recovery of a quadratic analytic pencil. Issue 6 (3rd June 2021)

• Record Type: Journal Article
• Authors: Başkaya, Elif; Boumenir, Amin
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 6(2021)
• Page Start: 882
• Page End: 902
• Publication Date: 2021-06-03
• Subjects: Inverse problems -- quadratic pencil operator -- numerical reconstruction algorithm; Primary 65J22 -- 65F18 -- 49N45; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2020.1814281
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : We are concerned with the inverse spectral problem for a quadratic pencil operator. We show that one given spectrum is enough for its reconstruction in the case of one analytic potential. To do so we first prove few identities between the Taylor coefficients of the sought function and the Taylor coefficients of the characteristic function of the operator, whose zeros are the given eigenvalues. The method leads to solving an upper triangular nonlinear algebraic system, which is easily solved by Gaussian elimination. Convergence of the algorithm is proven in case p is a polynomial and several examples are used at the end to illustrate the accuracy and speed of the algorithm.