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Lot 148
VON NEUMANN, JOHN, VALENTINE BARGMANN and DEANE MONTGOMERY. Solution of Linear Systems of High Order. [Princeton, NJ]: Institute for Advanced Study, October 10, 1946.
4 June 2014, 13:00 EDT
New YorkSold for US$1,500 inc. premium
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VON NEUMANN, JOHN, VALENTINE BARGMANN and DEANE MONTGOMERY.
Solution of Linear Systems of High Order. [Princeton, NJ]: Institute for Advanced Study, October 10, 1946.
4to. Reproduced typescript. [2], 86 pp. Original buff printed wrappers, light wear and soiling at spine, a few ink marks on fore-edge.
Provenance: Jeremy Norman.
FIRST EDITION. Von Neumann recognized early on that the electronic digital computer could be used to expand the domain of numerical analysis, but that new numerical methods would have to be developed in order to use computers effectively. One of the first problems von Neumann tackled in his investigation of computer-oriented numerical analysis was the solution of linear systems of high order. This topic had been examined earlier by the mathematician Harold Hotelling, who in a 1943 paper discussing the use of punched-card equipment in the solution of linear equations ("Some new methods in matrix calculation, "Annals of Mathematical Statistics 14: 1-34) had warned against the possibility of error accumulation if elimination methods such as Gauss's were used. Hotelling 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. Origins of Cyberspace 955.
4to. Reproduced typescript. [2], 86 pp. Original buff printed wrappers, light wear and soiling at spine, a few ink marks on fore-edge.
Provenance: Jeremy Norman.
FIRST EDITION. Von Neumann recognized early on that the electronic digital computer could be used to expand the domain of numerical analysis, but that new numerical methods would have to be developed in order to use computers effectively. One of the first problems von Neumann tackled in his investigation of computer-oriented numerical analysis was the solution of linear systems of high order. This topic had been examined earlier by the mathematician Harold Hotelling, who in a 1943 paper discussing the use of punched-card equipment in the solution of linear equations ("Some new methods in matrix calculation, "Annals of Mathematical Statistics 14: 1-34) had warned against the possibility of error accumulation if elimination methods such as Gauss's were used. Hotelling 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. Origins of Cyberspace 955.

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