By Bernd Simeon
On September 18th, Werner C. Rheinboldt, one of the pioneers of numerical analysis, will turn 90. On the occasion of this anniversary, I would like to draw attention to Rheinboldt’s outstanding scientific oeuvre that covers many fields and often laid the foundation for future developments. Three prominent examples are as follows:
- His groundbreaking work on the numerical solution of systems of nonlinear equations. Everybody in numerical analysis likely knows, or has at least heard of, Iterative Solution of Nonlinear Equations in Several Variables by Rheinboldt and the late James M. Ortega. It was published in 1970 and reprinted by SIAM in 2000. Almost 10,000 citations have been counted for this seminal work.
- A posteriori error analysis for finite elements began with the paper “Error estimates for adaptive finite element computations” by Ivo Babuˆska and Rheinboldt. It was published in the SIAM Journal on Numerical Analysis in 1978, and triggered an avalanche of research in the following decades.
- Rheinboldt very early perceived the importance of geometry in numerical analysis. This has currently become prominent in various fields, such as geometric numerical integration and iso-geometric analysis. But Rheinboldt had already used concepts from differential geometry to solve DAEs in the 1980s, as described in “Differential-algebraic systems as differential equations on manifolds,” which appeared in Mathematics of Computation in 1984.
Rheinboldt’s career stations include the Universities of Heidelberg and Freiburg, the National Bureau of Standards, the Universities of Syracuse and Maryland, the University of Pittsburgh, and finally the Technical University of Munich, where he became an honorary member of the Department of Mathematics after moving back to Germany in 2007. He served as president of SIAM from 1976 to 1978 and was a member of various councils, among them the Scientific Board of the Zuse Institute Berlin.
In the 1990s, I had the privilege to collaborate with Rheinboldt during two stays at the University of Pittsburgh. Speaking on behalf of numerical analysts worldwide, let me express our warm thanks to him for his outstanding work, his inspiration, and the deep insight that he shared with us.
Congratulations and “herzliche Glückwünsche!”
Bernd Simeon is a professor in the Department of Mathematics at the Technical University of Kaiserslautern.