F Schöpfer et al 2006 Inverse Problems 22 311 doi:10.1088/0266-5611/22/1/017
F Schöpfer, A K Louis and T Schuster
Show affiliationsWe introduce and discuss nonlinear iterative methods to recover the minimum-norm solution of the operator equation Ax = y in Banach spaces X, Y, where A is a continuous linear operator from X to Y. The methods are nonlinear due to the use of duality mappings which reflect the geometrical aspects of the underlying spaces. The space X is required to be smooth and uniformly convex, whereas Y can be an arbitrary Banach space. The case of exact as well as approximate and disturbed data and operator are taken into consideration and we prove the strong convergence of the sequence of the iterates.
47A52 Ill-posed problems, regularization
47L10 Algebras of operators on Banach spaces and other topological linear spaces
Issue 1 (February 2006)
Received 23 August 2005, in final form 13 December 2005
Published 30 January 2006
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