A revisit on Landweber iteration
Rommel Real, Qinian Jin
Abstract
Abstract In this paper we revisit the discrepancy principle for Landweber iteration for solving linear as well as nonlinear inverse problems in Banach spaces and prove a new convergence result which requires neither the Gâteaux differentiability of the forward operator nor the reflexivity of the image space. Therefore, we expand the applied range of the discrepancy principle for Landweber iteration to cover non-smooth ill-posed inverse problems and to handle the situation that the data is contaminated by various types of noise.
Topics & Concepts
MathematicsDifferentiable functionCover (algebra)Banach spaceConvergence (economics)Inverse problemInverseApplied mathematicsRange (aeronautics)Nonlinear systemOperator (biology)Space (punctuation)Pure mathematicsMathematical analysisComputer scienceGeometryGeneComposite materialTranscription factorRepressorMechanical engineeringEngineeringMaterials scienceOperating systemQuantum mechanicsEconomic growthPhysicsBiochemistryEconomicsChemistryNumerical methods in inverse problemsImage and Signal Denoising MethodsSparse and Compressive Sensing Techniques