The Grand Four. Affine Invariant globalizations of Newton's Method for Nonlinear Problems (Peter Deuflhard, Zuse Institute Berlin)

04.06.2018 10:45

Four affine invariance classes (affine covariance, affine contravariance, affine conjugacy, affine similarity) for nonlinear problems lead to four different classes of adaptive global Newton algorithms. Affine covariance applies to boundary value problems for differential equations (both ODEs and PDEs), affine contravariance applies to Fredholm integral equations of seconde kind, affine conjugacy leads to convex optimization, and, last but not least, affine similarity leads to pseudo-continuation methods for steady state problems in time dependent ODEs or PDEs. For the latter invariance class rather recent results are presented.

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