| 释义 |
Horner, n.2|ˈhɔːnə(r)|
The name of W. G. Horner (1786–1837), English mathematician, used attrib. and in the possessive (esp. in Horner's method) to designate a method for finding the real roots of a polynomial equated to zero by means of successive approximations.
It involves finding by trial the largest integer α1 less than the root (x); transforming the equation to one with a root x1 = x - α1 (or 10(x - α1), to avoid fractions); finding the largest one-place decimal (or integer) a2 less than the new root; and so on, each approximation a1, a2, etc., providing one digit of the solution.
1842Penny Cycl. XXIV. 341/1 The use of Horner's method is very much more easy than that of Newton. 1875L. Hensley Scholar's Algebra xiii. 197 Horner's process..is applicable to find the roots of equations of all degrees. 1879Encycl. Brit. VIII. 500/2 Horner's method (1819) gives the root as a decimal, figure by figure. 1913W. P. Milne Higher Algebra viii. 352 The determination of the two consecutive integers between which the required root of f2(x) = 0 lies is therefore an easy matter very early in the Horner approximating process. 1957K. S. Kunz Numerical Analysis ii. 23 The Horner method was devised to reduce such pencil work. 1966W. E. Grove Brief Numerical Methods i. 1 Horner's method is not used in computing, for it is designed for hand calculation. |