Dynamical systems method for solving operator equations

zbMath1245.37012MaRDI QIDQ874316

Alexander G. Ramm

Publication date: 5 April 2007

Published in: Mathematics in Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://www.sciencedirect.com/science/bookseries/00765392/208

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear differential equations in abstract spaces (34G20) Nonlinear ill-posed problems (47J06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Dynamical systems in numerical analysis (37N30) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

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Regularized continuous analog of the Newton method for monotone equations in a Hilbert space ⋮ THE DYNAMICAL SYSTEMS METHOD FOR SOLVING NONLINEAR EQUATIONS WITH MONOTONE OPERATORS ⋮ Dynamical systems method of gradient type for solving nonlinear equations with monotone operators ⋮ Stability of solutions to evolution problems ⋮ A dynamical Tikhonov regularization for solving ill-posed linear algebraic systems ⋮ General problems of explicit integration of differential inequalities ⋮ Unnamed Item ⋮ Inversion of the Laplace transform from the real axis using an adaptive iterative method ⋮ A stability result for abstract evolution problems ⋮ Dynamical systems method for solving nonlinear equations with monotone operators ⋮ Unnamed Item ⋮ Dynamical systems gradient method for solving ill-conditioned linear algebraic systems ⋮ Discrepancy principle for DSM. II ⋮ Some convergence results of a modified asymptotical regularization gradient method for nonlinear ill-posed operator equation ⋮ On the DSM Newton-type method ⋮ On the explicit integration of special types of differential inequalities ⋮ Global existence of solutions to differential equations ⋮ An iterative scheme for solving nonlinear equations with monotone operators ⋮ Dynamical systems gradient method for solving nonlinear equations with monotone operators

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