"On Bernoulli's Numerical Solution of Algebraic Equations", in Proceedings of the Royal Society of Edinburgh.

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.…