Numerical Inverting of Matrices of High Order II
[ Menasha, WI ]: American Mathematical Society 1951. First Edition. Volume 1 (Issues 1-2): [2], 286 pages + Volume 2 (Issues 1-2) [2], 334 pages + Vol 2 #6 : 839-998 pages. A collection of 5 issues of the Proceedings of the American Mathematical Society bound in one physical volume with thick boards and a thin cloth backing, with the original issue wrappers bound in. 8vo. Includes the noted article on pages [188]-202 pages in Vol 2, #2. An ex-library copy with bookplate, stamps to page edges, otherwise bright and clean. Near Fine. Boards. [24520]
This paper is a sequel to Goldstine and Von Neumann's important paper "Numerical Inverting of Matrices of High Order" published in 1947. The first paper was hailed by mathematician J. H. Wilkinson as "having laid the foundation of modern error analysis" (Goldstine 1972, p290-91). In the preface Goldstein and Von Neumann note that the first paper "derived rigorous error estimates in connection with inverting matrices of high order. In this paper we reconsider the problem from a probabilistic point of view and reassess our critical estimates in this light." Both papers deal with the trustworthiness of using the newly developed computers to do numerical analysis. Hotelling, Von Neumann and others were concerned with how to deal with the accumulating rounding errors in intermediate calculatings and whether the resulting solutions were sufficiently free of numerical instability to be useful. Turing also did work in this area.
See Origins of Cyberspace #957 (referencing the 1947 initial paper).
Price: $200.00