Calcolo (2011) 48: 47–59 DOI 10.1007/s10092-010-0027-4 Comparison of parameter choices in regularization algorithms in case of different information about noise level Uno Hämarik · Reimo Palm · Toomas Raus Received: 12 November 2009 / Accepted: 5 May 2010 / Published online: 25 September 2010 © Springer-Verlag 2010 Abstract We consider linear ill-posed problems in Hilbert space with noisy data. The noise level may be given exactly or approximately or there may be no information about the noise level. We regularize the problem using the Landweber method, the Tikhonov method or the extrapolated version of the Tikhonov method. For all three cases of noise information we propose rules for choice of the regularization parame- ter. Extensive numerical experiments show the advantage of the proposed rules over known rules, including the discrepancy principle, the quasioptimality criterion, the Hanke-Raus rule, the Brezinski-Rodriguez-Seatzu rule and others. Numerical com- parison also shows at which information about the noise level our rules for approxi- mately given noise level should be preferred to other rules. Keywords Ill-posed problem · Noise level · Regularization · Tikhonov method · Extrapolated Tikhonov method · Landweber method · Regularization parameter choice Mathematics Subject Classification (1991) Primary 65J20 · Secondary 47A52 1 Introduction Let A : X → Y be a linear bounded operator between real Hilbert spaces. We are interested in finding the minimum norm solution x ∗ of the equation Ax = y ∗ , y ∗ ∈ R(A). (1) This paper is part of special issue devoted to the 2nd Dolomites Workshop on Constructive Approximation and Applications, 2009. U. Hämarik ( ) · R. Palm · T. Raus Faculty of Mathematics and Informatics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia e-mail: uno.hamarik@ut.ee