Boundary effects on convergence rates for Tikhonov regularization
نویسندگان
چکیده
منابع مشابه
Convergence rates for Tikhonov regularization based on range inclusions
This paper provides some new a priori choice strategy for regularization parameters in order to obtain convergence rates in Tikhonov regularization for solving ill-posed problems Af0 = g0, f0 ∈ X, g0 ∈ Y , with a linear operator A mapping in Hilbert spaces X and Y. Our choice requires only that the range of the adjoint operator A∗ includes a member of some variable Hilbert scale and is, in prin...
متن کاملOptimal Convergence Rates for Tikhonov Regularization in Besov Scales
Abstract. In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates an...
متن کاملConvergence rates analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators
We investigate convergence rates of Tikhonov regularization for nonlinear ill-posed problems when both the right-hand side and the operator are corrupted by noise. Two models of operator noise are considered, namely uniform noise bounds and point-wise noise bounds. We derive convergence rates for both noise models in Hilbert and in Banach spaces. These results extend existing results where the ...
متن کاملConvergence rates and source conditions for Tikhonov regularization with sparsity constraints
This paper addresses the regularization by sparsity constraints by means of weighted lp penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of √ δ in the 2-norm for 1 < p ≤ 2 and in the 1-norm for p = 1 as soon as the unknown solution is sparse. The case p = 1 needs...
متن کاملOn fractional Tikhonov regularization
It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth, i.e., the approximate solution may lack many details that the desired exact solution might possess. Two different approaches, both referred to as fractional Tikhonov methods have been introduced to remedy this shortcoming. This paper investigates the convergence properties of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1988
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90001-9