A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems

DOI10.4171/ZAA/679zbMath0826.65053OpenAlexW2009666499MaRDI QIDQ1891946

Otmar Scherzer, Andreas Neubauer

Publication date: 26 November 1995

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/679

zbMATH Keywords

convergenceparameter estimationnonlinear operator equationnonlinear ill-posed problemssteepest 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 (21)

Modified minimal error method for nonlinear ill-posed problems ⋮ A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods ⋮ Numerical approximation of a Tikhonov type regularizer by a discretized frozen steepest descent method ⋮ 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 ⋮ Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces ⋮ Analysis of the Block Coordinate Descent Method for Linear Ill-Posed Problems ⋮ Convergence analysis of an optimally accurate frozen multi-level projected steepest descent iteration for solving inverse problems ⋮ A modified steepest descent method for solving non-smooth inverse problems ⋮ A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems ⋮ Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data ⋮ Convergence rate results for steepest descent type method for nonlinear ill-posed equations ⋮ A New Gradient Method for Ill-Posed Problems ⋮ Modified steepest descent method for nonlinear irregular operator equations ⋮ On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements ⋮ On a Family of Gradient-Type Projection Methods for Nonlinear Ill-Posed Problems ⋮ A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs ⋮ Iterative Solution Methods ⋮ The Averaged Kaczmarz Iteration for Solving Inverse Problems ⋮ An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints ⋮ Iterative processes of Fejér type in ill-posed problems with a priori information

Cites Work

• Iterative solution methods for inconsistent linear equations with nonself-adjoint operators
• A uniform approach to gradient methods for linear operator equations
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• On the Landweber iteration for 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

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