TY - GEN
A1 - Deuflhard, Peter
A1 - Nowak, Ulrich
A1 - Weiser, Martin
T1 - Affine Invariant Adaptive Newton Codes for Discretized PDEs
N2 - 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.
T3 - ZIB-Report - 02-33
KW - Affine invariant Newton methods
KW - global Newton methods
KW - inexact Newton methods
KW - adaptive trust region methods
KW - nonlinear partial differential equa
Y1 - 2002
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/700
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-7005
ER -