Regularization methods in Banach spaces / by Thomas Schuster [and others].

Includes bibliographical references (pages 265-279) and index.

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the BV-norm have recently become very popular. Meanwhile the most well-known methods have been investigated for linear and nonlinear operator equations in Banach spaces. Motivated by these facts the authors aim at collecting and publishing these results in a monograph.

Why to use Banach spaces in regularization theory? -- Geometry and mathematical tools of Banach spaces -- Tikhonov-type regularization -- Iterative regularization -- The method of approximate inverse