Newton–Raphsonn.
/ˌnjuːtn ˈrafs(ə)n/, U.S. /ˈn(j)utn ˈræfs(ə)n/ Mathematics.
attributive. Designating an iterative method for finding a numerical solution to an equation in one or more dimensions; esp. in Newton–Raphson iteration, Newton–Raphson method; Newton–Raphson formula n. the formula which is iterated in this method. Cf. Newton n. 1.The Newton–Raphson method of approximating the solution of an equation f(x) = 0, in a single variable, consists of picking an initial approximation x0 and then iterating according to the formula xi+1 = xi − f(xi)/f′(xi), each successive value xi being a closer approximation to the exact solution.
ΚΠ
1910 F. Cajori in Science 32 488 (heading) Fourier's improvement of the Newton-Raphson method of approximation anticipated by Mourraille.
1924 E. T. Whittaker & G. Robinson Calculus of Observ. vi. 84 (heading) The Newton–Raphson Method... In substantially this form it was given by Raphson in 1690; but the method is commonly called Newton's, because Newton had previously suggested a nearly related process.
1946 H. H. Goldstine in Moore School Lect. (1985) 84 Since we ignored the (Δx)2 terms, this is only an approximation to Δx, and our next estimate for x is thus xn + (Δx)n or xn+1 = xn − f(xn)/ f′(xn), which is the Newton–Raphson formula.
1968 E. T. Copson Metric Spaces viii. 115 There are other iterative processes for finding the real roots of an algebraic..equation..one of the most famous is the Newton–Raphson iteration.
1991 Acta Metallurgica et Materialia 39 2673/2 The nonlinear kinematic equation..can easily be solved by means of a Newton–Raphson technique both for a Taylor or a Relaxed Constraint approximation.
This is a new entry (OED Third Edition, September 2003; most recently modified version published online March 2022).
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