On the choice of the Tikhonov regularization parameter and the discretization level: a discrepancy-based strategy

DOI10.3934/ipi.2016.10.1zbMath1334.35416arXiv1410.6222OpenAlexW1480600243MaRDI QIDQ254777

Adriano De Cezaro, Jorge P. Zubelli, Vinicius V. L. Albani

Publication date: 16 March 2016

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6222

zbMATH Keywords

Tikhonov regularizationdiscrepancy principlesdiscrete settingregularization convergence rates

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Nonlinear ill-posed problems (47J06) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (13)

The Morozov’s principle applied to data assimilation problems ⋮ Stable reconstruction of the volatility in a regime-switching local-volatility model ⋮ Morozov principle for Kullback-Leibler residual term and Poisson noise ⋮ Space-Time Finite Element Methods for Distributed Optimal Control of the Wave Equation ⋮ An adaptive finite element method for distributed elliptic optimal control problems with variable energy regularization ⋮ The calibration of stochastic local-volatility models: an inverse problem perspective ⋮ CONVEX REGULARIZATION OF LOCAL VOLATILITY ESTIMATION ⋮ A novel fractional Tikhonov regularization coupled with an improved super-memory gradient method and application to dynamic force identification problems ⋮ Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization ⋮ A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles ⋮ A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems ⋮ A splitting strategy for the calibration of jump-diffusion models ⋮ DISCREPANCY SETS FOR COMBINED LEAST SQUARES PROJECTION AND TIKHONOV REGULARIZATION

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convex regularization of local volatility models from option prices: convergence analysis and rates
• Regularization methods in Banach spaces.
• Iterative regularization methods for nonlinear ill-posed problems
• Regularization of ill-posed problems: Optimal parameter choice in finite dimensions
• Statistical and computational inverse problems.
• On nonlinear projections in Banach spaces
• Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces
• Seismic tomography is locally ill-posed
• Online local volatility calibration by convex regularization
• Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems
• Discretization of variational regularization in Banach spaces
• Convergence rates for Morozov's discrepancy principle using variational inequalities
• Parameter choice in Banach space regularization under variational inequalities
• Joint additive Kullback–Leibler residual minimization and regularization for linear inverse problems
• Morozov's discrepancy principle and Tikhonov-type functionals
• Local ill-posedness and source conditions of operator equations in Hilbert spaces
• Calibration of the Local Volatility in a Generalized Black--Scholes Model Using Tikhonov Regularization
• Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators
• Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates

This page was built for publication: On the choice of the Tikhonov regularization parameter and the discretization level: a discrepancy-based strategy