TY - JOUR
T1 - Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations
AU - Argyros, Ioannis K.
AU - George, Santhosh
AU - Monnanda Erappa, Shobha
PY - 2017/12/1
Y1 - 2017/12/1
N2 - For the solution of nonlinear ill-posed problems, a Two Step Newton-Tikhonov methodology is proposed. Two implementations are discussed and applied to nonlinear ill-posed Hammerstein type operator equations KF(x) = y, where K defines the integral operator and F the function of the solution x on which K operates. In the first case, the Fre´ chet derivative of F is invertible in a neighbourhood which includes the initial guess x0 and the solution x^. In the second case, F is monotone. For both cases, local cubic convergence is established and order optimal error bounds are obtained by choosing the regularization parameter according to the the balancing principle of Pereverzev and Schock (2005).We also present the results of computational experiments giving the evidence of the reliability of our approach.
AB - For the solution of nonlinear ill-posed problems, a Two Step Newton-Tikhonov methodology is proposed. Two implementations are discussed and applied to nonlinear ill-posed Hammerstein type operator equations KF(x) = y, where K defines the integral operator and F the function of the solution x on which K operates. In the first case, the Fre´ chet derivative of F is invertible in a neighbourhood which includes the initial guess x0 and the solution x^. In the second case, F is monotone. For both cases, local cubic convergence is established and order optimal error bounds are obtained by choosing the regularization parameter according to the the balancing principle of Pereverzev and Schock (2005).We also present the results of computational experiments giving the evidence of the reliability of our approach.
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U2 - 10.1007/s12215-016-0254-x
DO - 10.1007/s12215-016-0254-x
M3 - Article
AN - SCOPUS:85035102279
SN - 0009-725X
VL - 66
SP - 303
EP - 323
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 3
ER -