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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 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 Â" 3 November 1967) was one of New Zealand's most eminent mathematicians. Seller Inventory # S6715
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Bibliographic Details
Title: "On Bernoulli's numerical solution of ...
Publisher: Neill, 1927, 1938., In: Proceedings of the Royal Society of Edinburgh, Vol. XLVI, 1925-1926; Vol. LVII, 1936-1937. Edinburgh:
Publication Date: 1927
Binding: Hardcover
Edition: 1st Edition
