Mon, 20 July, 2009, 17:15-18:15, Foyer
We consider ill-posed problem with linear continuous operator acting between Hilbert spaces. For finding approximate solution we use conjugate gradient type methods CGLS and CGME, minimizing in Krylov subspace the discrepancy or the error, respectively. If the noise level of data is known, we propose to take for the stopping index the minimum of certain expressions of stopping indexes from the discrepancy principle and from the monotone error rule. In case of roughly given or unknown noise level we propose to take for the stopping index the minimizer of certain functional in interval [1, N]. This functional is the product of decreasing function (difference of discrepancies on different iteration steps) and increasing function (which characterizes possible magnification of the data error on current iteration step) in method CGLS and discrepancy in method CGME. The endpoint N of the minimization interval is found from certain parameter choice rule (in CGME method and in CGLS method in case of roughly given noise level) or from increase condition of the functional to be minimized (in CGLS method in case of unknown noise level). Results of extensive numerical experiments are given.
Presentation slides (pdf, 105 KB)
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