A general heuristic for choosing the regularization parameter in ill-posed problems

For a variety of regularization methods, including Tikhonov regularization, Landweber iteration, $\nu $-method iteration, and the method of conjugate gradients, we develop and illustrate a heuristic for choosing an appropriate regularization parameter. Our choice requires no particular a priori knowledge, since the parameter is determined from computable information only. However, if an estimation for the noise level in the data is at hand, then this can be used as a justification. In contrast to known parameter choice heuristics, a posteriors error estimates for the computed approximations can be given. Numerical examples show that the new parameter choice rules are promising alternatives to known parameter choice rules.