Titlebook: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization; New Results in Moder Jens Flemming Book 2018

尽忠

Variational Source Conditions Yield Convergence RatesWe introduce variational source conditions and derive convergence rates for Tikhonov-type regularization methods.

少量

Existence of Variational Source ConditionsWe prove that variational source conditions are available in almost all situations.

BLOT

What Are Quadratic Inverse Problems?We introduce the notion of quadratic inverse problems, present some examples and discuss ill-posedness as well as some geometric properties of quadratic mappings.

发现

absorbed

Aren’t All Questions Answered?We collect several questions concerning sparsity promoting regularization which remained unanswered during the past years of extensive research in this field.

上下连贯

Sparsity and ,,-RegularizationIn this section we describe the basic ideas of sparsity promoting regularization techniques, introduce ..-regularization and briefly discuss alternative methods. In addition we have a first look at several examples which will appear again later on in the text.

growth-factor

Ill-Posedness in the ,,-SettingWe discuss ill-posedness of linear operator equations in the ..-setting and show that this setting makes all linear equations ill-posed in the sense of Nashed.

裙带关系

Convergence RatesWe derive asymptotic error estimates for the ..-distance between exact and ..-regularized solutions to linear operator equations. These estimates are based on variational source conditions.

丛林

Jens FlemmingPresents recent research results in a consistent notation.Contributes to two very active fields of research.Shows that variational source condition always yields convergence rate results

英寸