Obituary: Christian Reinsch

By Cleve Moler

Mathematician Christian Reinsch passed away on October 8, 2022, in Munich, Germany. Christian was born in 1934 in Chemnitz, in the German state of Saxony, and was 88 years old at the time of his death. He was a retired professor of numerical analysis at the Technical University of Munich (TUM), where he spent most of his professional career. While at TUM, he was a close associate of computer pioneer Friedrich Bauer.

Christian was an intensely private person who seldom traveled far from his home in Munich and rarely participated in international conferences; consequently, he is not very well known within the field. Nevertheless, he played a fundamental role in the development and implementation of algorithms for numerical linear algebra. Christian’s work in the 1960s and 1970s influenced much of the software for matrix computation that is used today on machines of all sizes, from personal laptops to national supercomputers.

Christian coauthored the Handbook for Automatic Computation, Volume II: Linear Algebra—a research monograph published by Springer­Verlag in 1971—with James H. Wilkinson [1]. Often known simply as the Handbook, the volume is a collection of papers by 19 different writers that were published between 1965 and 1970 in Springer’s Numerische Mathematik. Each paper focuses on an algorithm that solves systems of simultaneous equations or computes matrix eigenvalues and singular values. The programs were written in ALGOL 60, which was the standard language for algorithm publication at the time. Translations of many ALGOL codes into Fortran produced the EISPACK subroutine library and eventually inspired most of the modern software for dense, stored matrix computation.

Wilkinson and his colleagues at the National Physical Laboratory in the U.K. wrote roughly half of the ALGOL procedures in the Handbook, while Christian authored several procedures himself and reviewed and tested most—if not all—of the entire collection. Both the programming style and numerical robustness of the Handbook benefitted from his meticulous examination.

One of the most original and important contributions in the Handbook is Christian and Gene Golub's paper about the matrix singular value decomposition (SVD). Golub and William Kahan published the first practical method for computing the SVD in 1965, and Golub went on to make improvements to the SVD algorithms between 1965 and 1970 — as did Christian. Christian’s review work on the Handbook provided him access to the implicit tridiagonal QR techniques for matrix eigenvalues that Wilkinson and John Francis were investigating, so he adapted implicit QR with Wilkinson shifts to the singular value situation. Fritz Bauer, editor-in-chief of the Handbook, brokered a joint authorship that resulted in the Golub-Reinsch algorithm for computing the SVD.

In addition to his work in linear algebra, Christian has published several papers and algorithms on the topic of splines. He also created a computer graphics library for the Leibniz Supercomputing Center of the Bavarian Academy of Sciences and Humanities.

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References
[1] Wilkinson, J.H., & Reinsch, C. (1971). Handbook for automatic computation, volume II: Linear algebra. Berlin, Heidelberg: Springer-Verlag.

Cleve Moler is co-founder and chief mathematician at MathWorks. He was president of SIAM from 2007 to 2008.