A modified Tikhonov regularization for linear operator equations
Abbreviated Journal Title
Numer. Funct. Anal. Optim.
convergence and asymptotic order of the regularized solutions; error; analysis; first kind operator equation; ill-posed problem; modified; Tikhonov regularization; ILL-POSED PROBLEMS; PARAMETER; CHOICE; ERROR; Mathematics, Applied
We construct with the aid of regularizing filters a new class of improved regularization methods, called modified Tikhonov regularization (MTR), for solving ill-posed linear operator equations. Regularizing properties and asymptotic order of the regularized solutions are analyzed in the presence of noisy data and perturbation error in the operator. With some accurate estimates in the solution errors, optimal convergence order of the regularized solutions is obtained by a priori choice of the regularization parameter. Furthermore, numerical results are given for several ill-posed integral equations, which not only roughly coincide with the theoretical results but also show that MTR can be more accurate than ordinary Tikhonov regularization (OTR).
Numerical Functional Analysis and Optimization
"A modified Tikhonov regularization for linear operator equations" (2005). Faculty Bibliography 2000s. 5396.