On broyden's method for the regularization of nonlinear ill-posed problems

DOI10.1080/01630569808816860zbMath0914.65066OpenAlexW2041983486MaRDI QIDQ4221448

Barbara Kaltenbacher

Publication date: 7 June 1999

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569808816860

zbMATH Keywords

convergencenumerical testsHilbert spacesnonlinear ill-posed problemsstopping rulequasi-Newton methodBroyden's methoditerative regularization methods

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (10)

Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions ⋮ Lavrentiev's regularization method in Hilbert spaces revisited ⋮ On TSVD regularization for a Broyden-type algorithm ⋮ Simplified Levenberg-Marquardt method in Hilbert spaces ⋮ Error estimates for the simplified iteratively regularized Gauss-Newton method under a general source condition ⋮ On stable parameter estimation and forecasting in epidemiology by the Levenberg-Marquardt algorithm with Broyden's rank-one updates for the Jacobian operator ⋮ A generalization of continuous regularized Gauss–Newton method for ill-posed problems ⋮ Iterative Solution Methods ⋮ A two-stage method for nonlinear inverse problems ⋮ Iterative Regularization and Generalized Discrepancy Principle for Monotone Operator Equations

Cites Work

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• Quasi-Newton Methods, Motivation and Theory
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Some Newton-type methods for the regularization of nonlinear ill-posed problems
• Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems

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