Regularization of ill-posed operator equations: an overview

DOI10.1007/s41478-020-00263-9zbMath1468.65051OpenAlexW3046210810MaRDI QIDQ2047306

Yanyan Li

Publication date: 19 August 2021

Published in: The Journal of Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41478-020-00263-9

zbMATH Keywords

regularizationTikhonovill-posed problemssource conditionbackward heat equationleast-square solutionHilbert scalesoptimal rateArcangeliLavrentievMorozov

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05) Singular integral equations (45E99)

Related Items (1)

Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems

Cites Work

• Simplified iterated Lavrentiev regularization for nonlinear ill-posed monotone operator equations
• On improving error estimates for Tikhonov regularization using an unbounded operator
• On Morozov's method for Tikhonov regularization as an optimal order yielding algorithm
• A generalization of Arcangeli's method for ill-posed problems leading to optimal rates
• Arcangeli's Method for Fredholm Equations of the First Kind
• A unified treatment for Tikhonov regularization using a general stabilizing operator
• Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions
• The trade-off between regularity and stability in Tikhonov regularization
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