Approximation of Inverse Problems

摘要

This extended abstract gives an overview of the contents of a forthcoming research article to be published in the refereed literature [3]. In applications it is frequently of interest to solve inverse problems [10, 14]: to find u, an input to a mathematical model, given y an observation of (some components of, or functions of) the solution of the model. We have an equation of the form y = g(u)(1)to solve for u ∈ X, given y∈Y , where X, Y are Banach spaces. We someties refer to as the observation operator. We refer to y as data or observations. It is typical of inverse problems that they are ill-posed: there may be no solution, or the solution may not be unique and may depend sensitively on y. For this reason some form of regularization is often employed [5] to stabilize computational approximations.