Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations

DOI10.1134/S096554251510005XzbMath1331.65079OpenAlexW2196651796MaRDI QIDQ904385

Anatoly B. Bakushinsky, Mikhail Yu. Kokurin

Publication date: 13 January 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s096554251510005x

zbMATH Keywords

stabilityHilbert spaceiterative methodsiterative regularizationaveragingmean-square convergencerandom errorsnon-regular nonlinear operator equations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (6)

Analysis of the Influence of the Lagrange Multiplier on the Operation of the Algorithm for Estimating the Signal Parameters under a Priori Uncertainty ⋮ On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems ⋮ Iteratively regularized Gauss-Newton method for operator equations with normally solvable derivative at the solution ⋮ Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution ⋮ Low-cost numerical method for solving a coefficient inverse problem for the wave equation in three-dimensional space ⋮ Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations

Cites Work

• On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
• New method of stochastic approximation type
• Methods of the stochastic approximation type for solving linear incorrectly posed problems
• Statistical and computational inverse problems.
• Automatic training systems
• Iteratively Regularized Gauss–Newton Method for Nonlinear Inverse Problems with Random Noise
• On the Hàjek-Rènyi inequality
• On a Stochastic Approximation Theorem in a Hilbert Space and Its Applications
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