Karl Hessenberg

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

Life and work

Hessenberg studied electrical engineering at the Technische Hochschule Darmstadt 1925-1930. He received his doctorate in 1942 at Alwin Walther, the dissertation is entitled " The computation of eigenvalues ​​and solutions of linear systems of equations ".

According to Karl Hessenberg Hessenberg matrices which have been designated. Most is, even today, cited as the origin of this type of matrices, the dissertation of Hessenberg, eg in the book on matrices of Rudolf Zurmühl. In this case, the title is usually given as " solution of linear eigenvalue problems using the Hamilton - Cayley equation ". But have their origin Hessenberg matrices in a report of the IPM (Institute of Applied Mathematics ) Darmstadt. The title of the report is " treatment of linear eigenvalue problems using the Hamilton - Cayley equation ", ie almost that falsely assigned title of the dissertation. Publisher is the report of 1940.

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

Hessenberg's life and work was made possible by the research of Japanese scientist Seiji Fujino, starting with a query in the NA Digest, brought back to consciousness of numerical mathematicians. Developed by Hessenberg method was further developed by James Hardy Wilkinson in his book "The Algebraic Eigenvalue Problem " to the so-called generalized Hessenberg method.

The method of Hessenberg, as well as the generalized versions of Wilkinson belong to the class of Krylov subspace methods. Although the process of Hessenberg is one of the oldest methods of this kind, it seemed full ten years before the publication of Cornelius Lanczos and Hestenes & Stiefel, it still has a certain relevance. Building on the original method of Hessenberg Hassane Sadok has 1999 residuals minimizing method CMRH called ( Changing Minimal Residual method based on the Hessenberg process) developed, which represents an alternative to the solution of crowded systems of linear equations using the Gaussian elimination method.