Role of Hilbert Scales in Regularization Theory

DOI10.1007/978-81-322-2488-4_13zbMath1327.65270OpenAlexW1174022327MaRDI QIDQ3449722

M. Thamban Nair

Publication date: 5 November 2015

Published in: Semigroups, Algebras and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-81-322-2488-4_13

zbMATH Keywords

regularizationTikhonov regularizationdiscrepancy principleill-posed problemHilbert scalesill-posed equationsGelfand tripleSobolev scalesorder optimal Gelfand triplesource sets

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for integral transforms (65R10) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Fredholm integral equations (45B05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (2)

Simplified generalized Gauss-Newton method for nonlinear ill-posed operator equations in Hilbert scales ⋮ A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On improving error estimates for Tikhonov regularization using an unbounded operator
• Regularization with differential operators. I: General theory
• 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
• Morozov's discrepancy principle under general source conditions
• The limited-view problem in diffraction tomography
• Regularization in Hilbert scales under general smoothing conditions
• Error bounds for tikhonov regularization in hilbert scales
• High-contrast impedance tomography
• The trade-off between regularity and stability in Tikhonov regularization

This page was built for publication: Role of Hilbert Scales in Regularization Theory