On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces

DOI10.1515/fca-2019-0039zbMath1478.65059arXiv1812.09734OpenAlexW3100612269MaRDI QIDQ2328632

Ye Zhang, Bernd Hofmann

Publication date: 10 October 2019

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.09734

zbMATH Keywords

convergence ratesfractional derivativesaccelerationsource conditionsstopping rulesasymptotical regularizationlinear ill-posed operator equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (12)

A fractional Landweber iterative regularization method for stable analytic continuation ⋮ Stochastic asymptotical regularization for linear inverse problems ⋮ The Levenberg-Marquardt regularization for the backward heat equation with fractional derivative ⋮ On the asymptotical regularization with convex constraints for nonlinear ill-posed problems ⋮ On the acceleration of optimal regularization algorithms for linear ill-posed inverse problems ⋮ On a class of linear regression methods ⋮ A Tikhonov regularization method for Cauchy problem based on a new relaxation model ⋮ On a weighted time-fractional asymptotical regularization method ⋮ Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems ⋮ Optimal-order convergence of Nesterov acceleration for linear ill-posed problems* ⋮ Perturbation analysis of \(L_{1-2}\) method for robust sparse recovery ⋮ A new class of accelerated regularization methods, with application to bioluminescence tomography

Uses Software

• FracPECE

Cites Work

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