An Optimal Stopping Rule for the v-Method for Solving Ill-Posed Problems, Using Christoffel Functions Original Research Article

We design an order-optimal stopping rule for the v-method for solving ill-posed problems with noisy data. The construction of the v-method is based on a sequence of Jacobi polynomials, and the stopping rule is based on a sequence of related Christoffel functions. The motivation for our stopping criterion arises from a careful comparison between the iterates of the v-method and the approximations obtained from iterated Tikhonov regularization with (noninteger) order v. The convergence results rely on asymptotic properties of the Christoffel functions.