Bernoullis Numerical Solution Algebraic Equations by Aitken (2 results)
More imagesPublished by Neill, 1927, 1938., In: Proceedings of the Royal Society of Edinburgh, Vol. XLVI, 1925-1926; Vol. LVII, 1936-1937. Edinburgh: 1927
- Hardcover
- First Edition
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Two volumes. 8vo. Pages 289-305; 36-45; 172-181; 269-304. [Entire volume: viii, 458; vii, 520 pp.] A few figs. and tables. Quarter brown morocco, morocco corners, marbled sides, raised bands, gilt spine. Blind stamp of the Carnegie Institution of Washington, Mount Wilson Observatory. Fine. FIRST EDITIONS. "The aim of the present… paper is to extend Daniel Bernoulli's method of approximating to the numerically greatest root of an algebraic equation. On the basis of the extension here given it now becomes possible to make Bernoulli's method a means of evaluating not merely the greatest root, but all the roots of an equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots. In particular, the evaluation of complex roots is extremely simple, whatever the number of pairs of such roots. There is also a way of deriving from a sequence of approximations to a root successive sequences of ever-increasing rapidity of convergence." â" Cambridge Univ. Press. / A. C. Aitken, of the Mathematical Institute, University of Edinburgh, made important contributions in the field of numerical analysis, powerful methods for the solution of general mathematical problems in numerical terms. These methods, in turn, provided the logical basis for modern computers. A practical method for finding a numerical value of f(x), for a given value of x, when several values of x and f(x) are known, as Aitken's process of iteration. These methods are well adapted to computing machinery. It consists of an iteration of the familiar process of linear interpolation. These and other methods, such as that in Aitken's paper on Bernoulli's method for solving algebraic equations, are offered here. Engineering Research Associates, High-speed computing devices, pp. 108-109; Fox, "Early numerical analysis in the United Kingdom," in Nash, A history of scientific computing, p. 284; Hartree, Numerical analysis, pp. 84 & 280. Alexander Craig "Alec" Aitken FRS FRSE FRSL FRSNZ (1 April 1895 â" 3 November 1967) was one of New Zealand's most eminent mathematicians.
Published by Robert Grant & Son. 1926
- Softcover
Seller: JF Ptak Science Books, Hendersonville, NC, U.S.A.JF Ptak Science Books
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Soft cover. Condition: Very Good. AITKEN, A.C. "On Bernoulli's Numerical Solution of Algebraic Equations", in Proceedings of the Royal Society of Edinburgh, Session 1925-1926. Edinburgh, Robert Grant & Son, 1926. The Aitken occupies pp 289-305 in the issue of pp 245-320. Original wrappers. Provenance: small oval rubber stamp on…front cover for the Army Medical Library. This work--coming early in Aitken's career as his fourth publication--has been cited 600+ times and is a classic in the history of computation. See Bultheel & Cools, "Birth of Numerical Analysis", p. 19. Unopened. VG copy. [++] "The aim of the present paper is to extend Daniel Bernoulli's method of approximating to the numerically greatest root of an algebraic equation. On the basis of the extension here given it now becomes possible to make Bernoulli's method a means of evaluating not merely the greatest root, but all the roots of an equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots. In particular, the evaluation of complex roots is extremely simple, whatever the number of pairs of such roots. There is also a way of deriving from a sequence of approximations to a root successive sequences of ever-increasing rapidity of convergence."--Abstract.
