On weakly bounded noise in ill-posed problems
Abbreviated Journal Title
NONLINEAR TIKHONOV REGULARIZATION; HILBERT SCALES; INVERSE PROBLEMS; CONVERGENCE-RATES; EQUATIONS; PRINCIPLE; Mathematics, Applied; Physics, Mathematical
We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the error in the data converges strongly to zero, we only assume a type of weak convergence. Under the source conditions that are usually assumed in the presence of convex constraints, we derive optimal convergence rates for convexly constrained Phillips-Tikhonov regularization. We also discuss a version of the Lepskii method for selecting the regularization parameter.
"On weakly bounded noise in ill-posed problems" (2009). Faculty Bibliography 2000s. 1511.