Regularizing algorithms for solving nonlinear ill-posed problems of vibrational spectroscopy

G. M. Kuramshina^a, A. G. Yagola<sup>b

a</sup> Department of Physical Chemistry Faculty of Chemistry Lomonosov Moscow State University Moscow 119991, Russia Fax: (7)(495)932-8846
^b Department of Mathematics Faculty of Physics Lomonosov Moscow State University Moscow 119991, Russia Fax: (7)(495)932-8820

Abstract: Inverse problems of molecular force field calculation arising as a result of data processing in vibrational spectroscopy belong to the class of nonlinear ill-posed problems. In this paper we discuss the main mathematical results obtained within the theory of regularization for solving these problems. Different algorithms on the basis of regularizing methods were proposed for solving nonlinear ill-posed problems of molecular force field calculations and implemented in the software package SPECTRUM.

Keywords: inverse problem, nonlinear ill-posed problem, theory of regularization, vibrational spectra, molecular force field.

MSC: 49N45, 65F18, 92E10.

Received: 01.12.2016

Language: English