A Stopping Criterion for Classical Iterative Methods in Inexact Affine{invariant Newton Techniques
نویسندگان
چکیده
We present a method for the computation of stopping criterion for linear classical iterations in inexact aane-invariant Newton techniques. We show that the same methodology does not hold for non-classical iterative methods.
منابع مشابه
Affine Invariant Adaptive Newton Codes for Discretized PDEs
The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and in...
متن کاملConvergence behaviour of inexact Newton methods
In this paper we investigate local convergence properties of inexact Newton and Newton-like methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm are provided. For a special case the results are affine invariant.
متن کاملAccelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations
Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general framework that includes many well-known techniques for solving linear and nonlinear systems, as well as new...
متن کاملComparing different stopping criteria for fuzzy decision tree induction through IDFID3
Fuzzy Decision Tree (FDT) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. When a FDT induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. Finding a proper threshold value for a stopping crite...
متن کاملInexact Kleinman-Newton Method for Riccati Equations
In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...
متن کامل