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Volume 3, Issue 3, 1 December 2019, Pages 257-275
Abstract. An iteratively regularized projection method, which converges quadratically, is considered for stable approximate solutions to a nonlinear ill-posed operator equation , where is a nonlinear monotone operator defined on the real Hilbert space We assume that only a noisy data with are available. Under the assumption that the Fréchet derivative of is Lipschitz continuous, a choice of the regularization parameter using an adaptive selection of the parameter and a stopping rule for the iteration index using a majorizing sequence are presented. We prove that, under a general source condition on the error between the regularized approximation (, where is an orthogonal projection on to a finite dimensional subspace of ) and the solution is of optimal order.
How to Cite this Article:
Ioannis K. Argyros, Santhosh George, Expanding the applicability of an iterative regularization method for ill-posed problems, J. Nonlinear Var. Anal. 3 (2019), 257-275.