AN OPTIMAL STOPPING RULE FOR THE NU-METHOD FOR SOLVING ILL-POSED PROBLEMS, USING CHRISTOFFEL FUNCTIONS

We design an order-optimal stopping rule for the nu-method for solving ill-posed problems with noisy data. The construction of the nu-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 nu-method and the approximations obtained from iterated Tikhonov regularization with (noninteger) order nu. The convergence results rely on asymptotic properties of the Christoffel functions. (C) 1994 Academic Press, Inc.