Solution of Linear Systems of High Order.

Notes

First edition of this report on computer-oriented numerical analysis, a key document in charting the early development of von Neumann's understanding of the work of Carl Friedrich Gauss. The statistician Harold Hotelling had discredited Gauss's approach to numerical analysis and "advocated using an iterative method to eliminate numerical instability in the solution of large linear systems, a conclusion that von Neumann, Bargmann, and Montgomery supported in the present paper. Von Neumann changed his mind on this a year later... He concluded that he had been overly pessimistic in accepting Harold Hotelling's conjecture that elimination methods such as Gauss's were unsuitable for these types of problems" (Origins of Cyberspace, pp. 477, 479-80). The resulting paper co-authored with Herman H. Goldstine, "Numerical inverting of matrices of high order" (1947), reaffirmed von Neumann's belief in the stability of Gaussian procedure; it is considered to have laid the foundation of modern error analysis. This report was prepared in accordance with Contract NORD-9596 between the Bureau of Ordnance, Navy Department and the Institute for Advanced Study.