Friedrich Bauer

Fritz Bauer, eminent German computer scientist and last surviving member of the organizing committee of the 1964 Gatlingburg Conference on Numerical Algebra, passed away on March 26 at the age of 90.


The Photograph

Execute these commands in any MATLAB since version 4.0, 1992.

   load gatlin
   axis off

This is the organizing committee of the 1964 Conference on Numerical Algebra in Gatlinburg, Tennessee. They are J. H. Wilkinson, Wallace Givens, George Forsythe, Alston Householder, Peter Henrici, and Friedrich Bauer. Bauer, on the far right, was the youngest member of the committee.

I obtained the 8-by-10, black-and-white, glossy photo when I attended the conference as a grad student. It was my first big professional meeting and the first of what has become an important series of meetings for me and MATLAB. I kept the photo in my files until 1992 when we could handle images in MATLAB. I scanned in the photo and it became one of our first example images.

All six of the men in the photo have made contributions that have had a lasting impact on numerical analysis, computer science, and, ultimately, MATLAB. And all six have influenced my life personally.

Herr Professor Bauer

Credit: <>

Friedrich Bauer, 1924-2015.

My friend Walter Gander has written an obituary of Bauer for the Communications of the ACM that I reference below. Bauer was born on June 10, 1924, in Regensburg, Germany. After World War II, he studied mathematics and physics at Ludwig Maximillians Universitat in Munich, where he received his Ph.D. in 1951.

Bauer was involved in the early development of computers in Germany. These included STANISLAUS, a relay based computer, in 1951, and PERM, a stored program electronic computer, in 1952-56.

Bauer held a professorship in mathematics at Mainz from 1958 until 1963. He then returned to Munich and the Munich Institute of Technology, where he spent the remainder of his professional career. He advised 39 PhD students before he retired in 1989.


Bauer, together with his colleague Klaus Samelson, invented the stack for use in parsing and evaluating algebraic expressions. Today this is also known as a LIFO, for Last In First Out, data structure.

Computer Science and Software Engineering

Bauer was an early advocate for the recognition of computer science as an independent discipline in German universities. He also advocated the notion of software engineering and, in 1972, suggested a definition.

Establishment and use of sound engineering principles to obtain, economically, software that is reliable and works on real machines efficiently.

This definition of software engineering is now universally quoted.


Bauer was one of the principal authors of the reports on the programming languages International Algebraic Language, IAL, also known as Algol 58, and Algorithmic Language 1960, Algol 60. Wilkinson's research on algorithms for matrix eigenvalues was published in Numerische Mathematik in Algol. Equally important, Algol led directly to Niklaus Wirth's pedagogical programming language PL/0, which led to the design of MATLAB. So Bauer had a strong influence on the design of the MATLAB language. I want to tell that story in my next blog post.


The numerical linear algebra community represented by our Gatlinburg photo was very closely knit. Bauer visited Oak Ridge several times. He visited Stanford for a quarter in 1967, stayed in Gene Golub's home, and gave a course where he lectured on the theory of norms. Bauer and Householder were close friends. In fact, Householder married Bauer's wife's older sister, Heidi.

Numerical Analysis

One of my favorite results from the numerical analysis that underlies matrix computation is the Bauer-Fike Theorem. It tells how close a computed eigenvalue is to an exact one. You need to be able to estimate the condition of the eigenvectors.

Bauer-Fike Theorem. Let $A$ be a diagonalizable matrix and let $V$ be its matrix of eigenvectors. Let $\mu$ and $x$ be an approximate eigenvalue and eigenvector with corresponding residual

$$ r = A x - \mu x $$

Then there exists $\lambda$, an exact eigenvalue of $A$, such that

$$ | \lambda - \mu | \le \kappa(V) \frac{||r||}{||x||} $$


$$ \kappa(V) = ||V|| ||V^{-1}|| $$

is the condition number of the eigenvector matrix.

There is a proof in Wikipedia.

Bavarian Alpinist

I didn't know Fritz Bauer well. I only saw him for a few days every three years at the Gatlinburg/Householder meetings. But the memories are vivid.

In 1996, Householder XIII was in Pontresina, Switzerland. The traditional Wednesday afternoon "break" consisted of an excursion to the Morteratsch Glacier. The adventurous among the world's leading numerical analysts took off on a hike down the glacier, back to the base. I did not want to be left out, although the hiking boots I had hauled to Europe were not in good shape. Halfway down the glacier, a few of us were falling behind. Here comes Fritz and a couple of others. They had taken an longer, more difficult route to inspect a waterfall. He was over seventy years old at the time, but he looked great. He is an avid hiker and was in terrific shape. He was wearing the traditional Alpine lederhosen and first-rate hiking boots.

That was almost twenty years ago, but that's how I'll remember him. Fritz Bauer -- Computer Science Renaissance Man and Bavarian Alpinist.


Walter Gander, "The Life of a Computer Pioneer", Blog@CACM, April 13, 2015, <>

Wikipedia, "Bauer-Fike Theorem", <>

Published with MATLAB® R2015a

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