Herman Goldstine John Neumann (6 results)

Paperback. Condition: New. Print on Demand. Excerpt from Planning and Coding of Problems for an Electronic Computing Instrument. About the Publisher, Forgotten Books publishes hundreds of thousands of rare and classic books. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value. The digital edition of all books may be viewed on our website before purchase. print-on-demand item.

Softcover. Condition: Near Fine. First printing. A near fine, clean copy. Original wrappers. The complete issue. This "remarkably original" (D.S.B.) paper, the sole technical paper in this entire issue of the Bulletin of the American Mathematical Society, laid the foundation of modern error analysis in numerical computation. * 004886.

On algorithms for finding the characteristic values of a matrix suitable for use on large-scale electronic digital computers. Octavo. The complete volume, in original printed wrappers. Stain on front cover, library rubberstamp on first page of the periodical. Otherwise very good. Hook and Norman, 968.

Condition: Very Good. first edition, later printing (1951) (the first printing was in 1946); quarto, [vi], 23 pp., original stapled paper wrappers (softcover), minor crease to upper corner of pages and covers else very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Photos available upon request.

First edition. THE BIRTH OF MODERN NUMERICAL ANALYSIS. First edition, journal issues in the original printed wrappers, of two of von Neumann's major papers. "The 1947 paper by John von Neumann and Herman Goldstine, 'Numerical Inverting of Matrices of High Order' (Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous" (Bultheel & Cools). "Just when modern computers were being invented (those digital, electronic, and programmable), 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 concerning the accuracy of mechanized Gaussian elimination - but their paper was about more than that. Von Neumann and Goldstine described what they surmised would be the significant questions once computers became available for computational science, and they suggested enduring ways to answer them" (Grcar, p. 607). "In sum, von Neumann's paper contains much that is unappreciated or at least unattributed to him. The contents are so familiar, it is easy to forget von Neumann is not repeating what everyone knows. He anticipated many of the developments in the field he originated, and his theorems on the accuracy of Gaussian elimination have not been encompassed in half a century. The paper is among von Neumann's many firsts in computer science. It is the first paper in modern numerical analysis, and the most recent by a person of von Neumann's genius" (Vuik). Von Neumann & Goldstine's 1947 paper is here accompanied by its sequel (the 1947 paper comprises Chapters I-VII, the sequel Chapters VIII-IX), in which the authors reassess the error estimates proved in the first part from a probabilistic point of view. The only other copy of either paper listed on ABPC/RBH is the OOC copy of part I (both journal issue and offprint). "Before computers, numerical analysis consisted of stopgap measures for the physical problems that could not be analytically reduced. The resulting hand computations were increasingly aided by mechanical tools which are comparatively well documented, but little was written about numerical algorithms because computing was not considered an archival contribution. "The state of numerical mathematics stayed pretty much the same as Gauss left it until World War II" [Goldstine, The Computer from Pascal to Von Neumann (1972), p. 287]. "Some astronomers and statisticians did computing as part of their research, but few other scientists were numerically oriented. Among mathematicians, numerical analysis had a poor reputation and attracted few specialists" [Aspray, John von Neumann and the Origins of Modern Computing (1999), pp. 49-50]. "As a branch of mathematics, it probably ranked the lowest, even below statistics, in terms of what most university mathematicians found interesting" [Hodges, Alan Turing: the Enigma (1983), p. 316]. "In this environment John von Neumann and Herman Goldstine wrote the first modern paper on numerical analysis, 'Numerical Inverting of Matrices of High Order', and they audaciously published the paper in the journal of record for the American Mathematical Society. The inversion paper was part of von Neumann's efforts to create a mathematical discipline around the new computing machines. Gaussian elimination was chosen to focus the paper, but matrices were not its only subject. The paper was the first to distinguish between the stability of a mathematical problem and of its numerical approximation, to explain the significance in this context of the 'Courant criterium' (later CFL condition), to point out the advantages of computerized mixed precision arithmetic, to use a matrix decomposition to prove the accuracy of a calculation, to describe a 'figure of merit' for calculations that became the matrix condition number, and to explain the concept of inverse, or backward, error. The inversion paper thus marked the first appearance in print of many basic concepts in numerical analysis. "The inversion paper may not be the source from which most people learn of von Neumann's ideas, because he disseminated his work on computing almost exclusively outside refereed journals. Such communication occurred in meetings with the many researchers who visited him at Princeton and with the staff of the numerous industrial and government laboratories whom he advised, in the extemporaneous lectures that he gave during his almost continual travels around the country, and through his many research reports which were widely circulated, although they remained unpublished. As von Neumann's only archival publication about computers, the inversion paper offers an integrated summary of his ideas about a rapidly developing field at a time when the field had no publication venues of its own. "The inversion paper was a seminal work whose ideas became so fully accepted that today they may appear to lack novelty or to have originated with later authors who elaborated on them more fully. It is possible to trace many provenances to the paper by noting the sequence of events, similarities of presentation, and the context of von Neumann's activities" (Grcar, pp. 609-610). We are fortunate to have an account of the genesis and content of these two important papers in Goldstine's own words. In the years immediately following the end of World War II, Von Neumann, Goldstine and others instituted the 'electronic computer project' at the Institute for Advanced Study at Princeton, NJ. One of the first topics discussed "was the solution of large systems of linear equations, since they arise almost everywhere in numerical work.

4to, 6 + 42 leaves. Original buff wrapppers, crudely but effectively rebacked with pale card. Signature ?Newman? on upper wrapper, probably Professor M.H.A. Newman (1897?1984), mathematician and computer pioneer and one of Alan Turing?s professors at Cambridge; stamp of Imperial College London on fore-edge, spine and lower corner covered in clear adhesive tape over ?for Reference Only sticker?, shelf marks and stamp on title-page. Second, enlarged edition a year after the first. ?A few months after ENIAC had its first public demonstration (in February 1946), the three chief members of the IAS Electronic Computer Project issued their Preliminary Discussion?, a report to the Army Ordnance Department that represents the first published formal conceptual paper on the stored-program computer, if we call von Neumann?s informal First Draft a privately circulated working paper. The first edition of the Preliminary Report appeared in June 1946; a revised second edition, containing an expanded account of the arithmetic processes and a report of further experimental work, was issued in September 1947. This was followed by the three-part Planning and Coding of Problems? ?The Preliminary Report contains the first technical description of what is known as the von Neumann architecture, in which programs and data are stored in a comparatively slow-to-access storage medium, such as a hard disk; and work is performed on them in a fast, volatile random access-memory?? (from a long note in Hook & Norman, Origins of cyberspace, 959 (1).