700
eng
reportzib
0
2002-10-24
2002-10-24
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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 inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs.
02-33
701
urn:nbn:de:0297-zib-7005
Appeared in: P. Deuflhard: Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Springer 2004. Series Computational Mathemtics, 35
Peter Deuflhard
Ulrich Nowak
Martin Weiser
ZIB-Report
02-33
eng
uncontrolled
Affine invariant Newton methods
eng
uncontrolled
global Newton methods
eng
uncontrolled
inexact Newton methods
eng
uncontrolled
adaptive trust region methods
eng
uncontrolled
nonlinear partial differential equa
Informatik, Informationswissenschaft, allgemeine Werke
Systems of equations
Global methods, including homotopy approaches [See also 58C30, 90C30]
Computational Medicine
Deuflhard, Peter
Weiser, Martin
https://opus4.kobv.de/opus4-zib/files/700/ZR-02-33.ps
https://opus4.kobv.de/opus4-zib/files/700/ZR-02-33.pdf