TY - JOUR

T1 - Projection method for newton-tikhonov regularization for non-linear ill-posed hammerstein type operator equations

AU - Shobha, Monnanda Erappa

AU - George, Santhosh

PY - 2013

Y1 - 2013

N2 - An iteratively regularized projection scheme for the ill-posed Hammerstein type operator equation KF(x) = f has been considered. Here F : D(F)X X is a non-linear operator, K : X → Y is a bounded linear operator, X and Y are Hilbert spaces. The method is a combination of dis- cretized Tikhonov regularization and modified Newton's method. It is assumed that the Fŕechet derivative of F at x0 is invertible i.e., the ill-posedness of the operator KF is due to the ill-posedness of the linear operator K. Here x0 is an initial approximation to the solution x of KF(x) = f. Adaptive choice of the parameter suggested by Perverzev and Schock(2005) is employed in select- ing the regularization parameter α. A numerical example is given to test the reliability of the method.

AB - An iteratively regularized projection scheme for the ill-posed Hammerstein type operator equation KF(x) = f has been considered. Here F : D(F)X X is a non-linear operator, K : X → Y is a bounded linear operator, X and Y are Hilbert spaces. The method is a combination of dis- cretized Tikhonov regularization and modified Newton's method. It is assumed that the Fŕechet derivative of F at x0 is invertible i.e., the ill-posedness of the operator KF is due to the ill-posedness of the linear operator K. Here x0 is an initial approximation to the solution x of KF(x) = f. Adaptive choice of the parameter suggested by Perverzev and Schock(2005) is employed in select- ing the regularization parameter α. A numerical example is given to test the reliability of the method.

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U2 - 10.12732/ijpam.v83i5.6

DO - 10.12732/ijpam.v83i5.6

M3 - Article

AN - SCOPUS:84875383334

SN - 1311-8080

VL - 83

SP - 643

EP - 650

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

IS - 5

ER -