The grand four - affine invariant globalizations of Netwon's method

Abstract:

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, affine conjugacy leads to convex optimization, and, last but not least, affine similarity leads to pseudo-continuation methods for equilibrium problems in time dependent ODEs or PDEs. For the latter invariance class rather recent results are presented.

Biography:

1963-68: Studies of Pure Physics, TH Munich
1968: Diploma Degree in Physics, TH Munich
1969-73: Scientific Assistant in Mathematics, University of Cologne (with R. Bulirsch)
1972: Dissertation in Mathematics, University of Cologne
1973-78: Senior Scientific Assistant (Tenure) in Mathematics, TU Munich
1977: Habilitation in Mathematics, TU Munich
1978-86: Full Professor, University of Heidelberg, chair Numerical Analysis (following W. Romberg)
1986-2012: Full Professor FU Berlin, chair Scientific Computing
1986: Founder of ZIB as a scientific research institute
1987-2012: President of ZIB
2002: Co-founder of DFG Research Center Matheon
2002-2012: Member of the Executive Board of Matheon
2012-2014: Senior Professor, Numerische Analysis, Institut für Mathematik, Freie Universität Berlin
2015-2016: Senior Professor, Chaire Thématique FaciLe, ICS - Institut du Calcul et de la Simulation, Université Pierre et Marie Curie (UPMC), Sorbonne, Paris
2015-2018: Founding Director of Beijing Institute for Scientific and Engineering Computing (BISEC)