Title: The regularisation of inverse and ill-posed problems
Abstract: Physical phenomena may be modelled in operator theoretic terms and deriving the cause of a particular effect then corresponds to computing the inverse of the aforementioned operator. It is often the case, however, that the problem is “ill-posed”; for instance, if the operator is surjective as then there is no longer a continuous dependence of the solution and data. One subsequently approximates the solution by a parametric family of operators, where the parameter controls the trade-off between stability and accuracy. This elegant interplay between theory and application is the art of regularisation, the convergence analysis for which utilises functional calculus or convex analysis, depending on the setting.