TY - GEN
T1 - Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations
AU - Shobha, Monnanda Erappa
AU - George, Santhosh
PY - 2012
Y1 - 2012
N2 - Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.
AB - Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method.
UR - https://www.scopus.com/pages/publications/84865230052
UR - https://www.scopus.com/pages/publications/84865230052#tab=citedBy
U2 - 10.1007/978-3-642-32112-2_35
DO - 10.1007/978-3-642-32112-2_35
M3 - Conference contribution
AN - SCOPUS:84865230052
SN - 9783642321115
T3 - Communications in Computer and Information Science
SP - 293
EP - 301
BT - Eco-Friendly Computing and Communication Systems - International Conference, ICECCS 2012, Proceedings
T2 - International Conference on Eco-Friendly Computing and Communication Systems, ICECCS 2012
Y2 - 9 August 2012 through 11 August 2012
ER -