Introduction

This chapter presents an introduction to inverse and ill-posed problems with applications. The degree of ill-posedness is also defined in terms of the rate of decay of the singular values of the governing, usually linear and compact, operator that maps the set of unknowns into the measured data. The classification of inverse problems into boundary-value, initial-value, source/force, coefficient and geometry problems is made. The discrete case is briefly discussed in terms of the solutions of ill-conditioned systems of linear algebraic equations. The classical Tikhonov regularization and truncated singular value decomposition methods are introduced and the choice of the regularization parameter is discussed.