Lavrentiev's regularization method in Hilbert spaces revisited

Saturation of Regularization Methods in Hilbert Spaces

We prove saturation of methods for solving ill-posed problems in Hilbert spaces for a wide class regularization methods. It turns out, that under a certain convexity assumption, saturation is necessary. We provide easy to verify assumptions, which allow to calculate the rate, at which saturation occurs.

Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces

and Applied Analysis 3 Proposition 5. If the minimization (14) is consistent, then the strong lim ε→0 ω ε exists and is the minimum-norm solution of the minimization (14). Proof. For any ω ∈ Γ, we have

Regularization and iterative method for general variational inequality problem in hilbert spaces

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Full list of author information is available at the end of the article Abstract Without the strong monotonicity assumption of the mapping, we provide a regularization method for general variational inequality problem, when its solution set is related to a solution se...

Generalized Frames in Hilbert Spaces

FUSION FRAMES IN HILBERT SPACES

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.