Karl Hessenberg

Karl Adolf Hessenberg (born September 8, 1904 in Frankfurt am Main ; † February 22, 1959 there ) was a German electrical engineer and mathematician.

Live and act

Hessenberg studied electrical engineering at the Technical University of Darmstadt between 1925 and 1930. He received his doctorate in 1942 under Alwin Walther , the dissertation is entitled “The calculation of eigenvalues ​​and eigen solutions of linear systems of equations” .

The Hessenberg matrices were named after Karl Hessenberg . Even today, the dissertation of Hessenberg is usually cited as the origin of this type of matrix, e.g. B. in the book about matrices by Rudolf Zurmühl . The title is usually given as "Solving linear eigenvalue problems using the Hamilton-Cayley equation" . The Hessenberg matrices have their origin in a report by the IPM (Institute for Practical Mathematics) Darmstadt. The title of the report is "Treatment of linear eigenvalue problems with the help of the Hamilton-Cayley equation" , almost the title wrongly assigned to the dissertation. The report was published in 1940.

Karl Hessenberg is the brother of the composer Kurt Hessenberg and great-grandson of the doctor and children's book author Heinrich Hoffmann .

Hessenberg's life and work were only brought back to the consciousness of numerical mathematicians by the Japanese scientist Seiji Fujino, beginning with an inquiry in the NA Digest. The method developed by Hessenberg was further developed by James Hardy Wilkinson in his book "The Algebraic Eigenvalue Problem" into the so-called generalized Hessenberg method .

The Hessenberg method, like the generalized variants of Wilkinson, belong to the class of Krylow subspace methods . Although the Hessenberg method is one of the oldest of its kind (it appeared ten years before the publications of Cornelius Lanczos and Hestenes & Stiefel) it still has some topicality. Based on the original Hessenberg method, Hassane Sadok developed a residual-minimizing method (Changing Minimal Residual method based on the Hessenberg process, CMRH for short) in 1999, which represents an alternative to solving densely populated linear systems of equations using the Gaussian elimination method .

literature

• On the trail of a German scientist; Dr. Karl Hessenberg, who was forgotten by the historiography of numerics , Seiji Fujino, GAMM Mitteilungen Vol. 18, No. 2, 1995, pp. 112-114
• Who was Karl Hessenberg? , Seiji Fujino and Erhard Heil, INFORMATION Vol. 1, No. 1, 1998, pages 29-36
• The Algebraic Eigenvalue Problem , JH Wilkinson, 1965, Oxford University Press, pp. 377-382
• CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm , H. Sadok, Numerical Algorithms 20, 1999, pages 303-321

Web links

• Website about Karl Hessenberg, created by Brigitte Bossert, daughter of Karl Hessenberg, with handwritten curriculum vitae and PDF files of the dissertation and the report
• Karl Hessenberg in the database of the Mathematics Genealogy Project