John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

  • Authors:
  • Joseph F. Grcar

  • Affiliations:
  • jfgrcar@comcast.net and na.grcar@na-net. ornl.gov

  • Venue:
  • SIAM Review
  • Year:
  • 2011

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Abstract

Just when modern computers (digital, electronic, and programmable) were being invented, John von Neumann and Herman Goldstine wrote a paper to illustrate the mathematical analyses that they believed would be needed to use the new machines effectively and to guide the development of still faster computers. Their foresight and the congruence of historical events made their work the first modern paper in numerical analysis. Von Neumann once remarked that to found a mathematical theory one had to prove the first theorem, which he and Goldstine did for the accuracy of mechanized Gaussian elimination—but their paper was about more than that. Von Neumann and Goldstine described what they surmized would be the significant questions once computers became available for computational science, and they suggested enduring ways to answer them.