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A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations
-
Santhosh George
and
Atef Ibrahim Elmahdy
Published/Copyright:
January 1, 2012
Abstract
In this paper, we consider an iterative method for the approximate solution of the nonlinear ill-posed operator equation Tx = y. The iteration procedure converges quadratically to the unique solution of the equation for the regularized approximation. It is known that (Tautanhahn (2002)) this solution converges to the solution of the given ill-posed operator equation. The convergence analysis and the stopping rule are based on a suitably constructed majorizing sequence. We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining an optimal order error estimate.
Keywords: nonlinear ill-posed operator; monotone operator; majorizing sequence; quadratic convergence
Received: 2010-07-22
Revised: 2010-12-13
Accepted: 2011-04-15
Published Online: 2012
Published in Print: 2012
© Institute of Mathematics, NAS of Belarus
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Keywords for this article
nonlinear ill-posed operator;
monotone operator;
majorizing sequence;
quadratic convergence
Articles in the same Issue
- Efficient Preconditioners for Large Scale Binary Cahn-Hilliard Models
- Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs
- A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations
- Exponentially Convergent Functional-discrete Method for Eigenvalue Transmission Problems with a Discontinuous Flux and the Potential as a Function in the Space L_1
- A FETI-DP Method for Crouzeix-Raviart Finite Element Discretizations
- An Approximation Method Based on Matrix Formulated Algorithm for the Heat Equation with Nonlocal Boundary Conditions
- Error Estimates for Approximations of American Put Option Price
