Convergence rate results for steepest descent type method for nonlinear ill-posed equations

DOI10.1016/j.amc.2016.09.009zbMath1411.65078OpenAlexW2525418510MaRDI QIDQ1734312

M. Sabari, Santhosh George

Publication date: 27 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2016.09.009

zbMATH Keywords

nonlinear ill-posed problemdiscrepancy principleregularization methodsteepest descent methodminimal error method

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 (7)

Modified minimal error method for nonlinear ill-posed problems ⋮ A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods ⋮ A Discretizing Levenberg-Marquardt Scheme for Solving Nonlinear Ill-Posed Integral Equations ⋮ A modified steepest descent scheme for solving a class of parameter identification problems ⋮ A modified convergence analysis for steepest descent scheme for solving nonlinear operator equation ⋮ A modified steepest descent method for solving non-smooth inverse problems ⋮ A New Gradient Method for Ill-Posed Problems

Uses Software

• TIGRA

Cites Work

• The instability of some gradient methods for ill-posed problems
• A minimal error conjugate gradient method for ill-posed problems
• Iterative solution methods for inconsistent linear equations with nonself-adjoint operators
• A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
• Irregular nonlinear operator equations: Tikhonov's regularization and iterative approximation
• A class of iterative methods of conjugate gradient type
• Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976
• TIGRA an iterative algorithm for regularizing nonlinear ill-posed problems
• A convergence analysis of a method of steepest descent and a two–step algorothm for nonlinear ill–posed problems
• Steepest descent for singular linear operators with nonclosed range
• On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations
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