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A discrepancy principle for Tikhonov regularization with approximately specified data

M. Thamban Nair, Eberhard Schock (1998)

Annales Polonici Mathematici

Many discrepancy principles are known for choosing the parameter α in the regularized operator equation ( T * T + α I ) x α δ = T * y δ , | y - y δ | δ , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and T * y δ are approximated by Aₙ and z δ respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable...

A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation

O. Awono, J. Tagoudjeu (2010)

Mathematical Modelling of Natural Phenomena

We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...

A study of Galerkin method for the heat convection equations

Polina Vinogradova, Anatoli Zarubin (2012)

Applications of Mathematics

The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained.

Adaptive wavelet methods for saddle point problems

Stephan Dahlke, Reinhard Hochmuth, Karsten Urban (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator....

An application of the induction method of V. Pták to the study of regula falsi

Florian-Alexandru Potra (1981)

Aplikace matematiky

In this paper we introduce the notion of " p -dimensional rate of convergence" which generalizes the notion of rate of convergence introduced by V. Pták. Using this notion we give a generalization of the Induction Theorem of V. Pták, which may constitute a basis for the study of the iterative procedures of the form X n + 1 = F ( x n - p + 1 , X n - p + 2 , ... , x n ) , n = 0 , 1 , 2 , ... . As an illustration we apply these results to the study of the convergence of the secant method, obtaining sharp estimates for the errors at each step of the iterative procedure.

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