Numerical Functional Analysis and Optimization · 2005 · 53 citations · 3 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisIterative SolversNumerical AlgorithmsNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityConvergenceIll-posed Problem RegularizationIll-posedness AnalysisSpectral ConvergenceStability Of Numerical SchemesSubject Classification
In this paper, we consider generalized Gauss–Newton's scheme for solving nonlinear unstable operator equation F(x) = f in a Hilbert space. In case of noisy data, we propose a novel a posteriori stopping rule and prove a convergence theorem under a source type condition on the solution. As a consequence of this theorem, we obtain convergence rates for various generating functions, θ = θ(λ, α), of a spectral parameter λ and α > 0. Key Words: Discrepancy principleIll-posed problemRegularizationMathematical Subject Classification: 47A5265F22 ACKNOWLEDGMENT This work is supported by RFFI grant (03-01-00352) and NSF grant (DMS-0207050).
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