John von Neumann

Macrae, Norman

doi:10.1007/978-3-0348-6064-2

Cited by 17 publications

(19 citation statements)

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“…Strangelove mode' (see (Strathern, 2002)): He sometimes put forward extremely naïve and politically unacceptable suggestions. Comparable to other strange behavioral traits of his personal life (see (Macrae, 1992)) this should be delegated to a discussion on his psychology and is largely independent of the Neumann-Morgenstern project. 16 Towards the end of his life he tried to isolate the essential elements of internal model-building by comparison with the human brain , and worked out the necessary general rules for self-reproducing automata.…”

Section: Advantages and Dangers Of Narrowing The Focus Of Game Theorymentioning

confidence: 99%

The Neumann-Morgenstern Project – Game Theory as a Formal Language for the Social Sciences

Hanappi¹

2013

Game Theory Relaunched

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Section: Advantages and Dangers Of Narrowing The Focus Of Game Theorymentioning

confidence: 99%

The Neumann-Morgenstern Project – Game Theory as a Formal Language for the Social Sciences

Hanappi¹

2013

Game Theory Relaunched

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“…Retrospectives of all his work are [39,111,136,286]. The main biography of von Neumann in English is [181]; biographies that focus on aspects of his career besides computing are [138,222]; and biographical sketches are [79,230]. Obituaries are [31,271].…”

Section: Notes On Biographymentioning

confidence: 99%

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

Grcar¹

2011

SIAM Rev.

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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.

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“…He is often described, in lay terms, as someone to whom we are indebted for inventing many useful branches of science and mathematics [13]. A modest conclusion to draw from this is that von Neumann had a special talent to inspire further research.…”

Section: Problemsmentioning

confidence: 99%

A matrix lower bound

Grcar

2002

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A matrix lower bound is defined that generalizes ideas apparently due to S. Banach and J. von Neumann. The matrix lower bound has a natural interpretation in functional analysis, and it satisfies many of the properties that von Neumann stated for it in a restricted case.Applications for the matrix lower bound are demonstrated in several areas. In linear algebra, the matrix lower bound of a full rank matrix equals the distance to the set of rank-deficient matrices. In numerical analysis, the ratio of the matrix norm to the matrix lower bound is a condition number for all consistent systems of linear equations. In optimization theory, the matrix lower bound suggests an identity for a class of min-max problems. In real analysis, a recursive construction that depends on the matrix lower bound shows that the level sets of continuously differentiable functions lie asymptotically near those of their tangents.

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John von Neumann

Cited by 17 publications

References 0 publications

The Neumann-Morgenstern Project – Game Theory as a Formal Language for the Social Sciences

The Neumann-Morgenstern Project – Game Theory as a Formal Language for the Social Sciences

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

A matrix lower bound

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