Modified steepest descent method for nonlinear irregular operator equations

DOI10.1134/S1064562415030187zbMath1334.65099MaRDI QIDQ498194

Vladimir V. Vasin

Publication date: 28 September 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceregularizationHilbert spacenonlinear operator equationoptimization problemiteration methodssteepest descent method

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 (3)

Regularized modified \(\alpha\)-processes for nonlinear equations with monotone operators ⋮ Regularized gradient algorithms for solving the nonlinear gravimetry problem for the multilayered medium ⋮ Two-stage method of construction of regularizing algorithms for nonlinear ill-posed problems

Cites Work

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• Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978
• A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
• Operators and iterative processes of Fejér type. Theory and applications.
• Irregular nonlinear operator equations: Tikhonov's regularization and iterative approximation
• Expanding the applicability of Tikhonov's regularization and iterative approximation for ill-posed problems
• Convexity of the Tikhonov functional and iteratively regularized methods for solving irregular nonlinear operator equations
• Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems

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