| 释义 |
Simpson's rule Math.|ˈsɪmpsən|
[Named after Thomas Simpson (1710–61), English mathematician, who proposed the rule in 1743 (Math. Dissertations 109).]
An arithmetical rule for estimating the area under a curve where the values of an odd number of ordinates, including those at the limits, are known: the approximate area is given by the sum of the first and last ordinates, double all the other odd ordinates, and quadruple all the even ordinates, multiplied by one third of the distance between adjacent ordinates. Also applied to other analogous rules (see quot. 1909).
1875B. Williamson Integral Calculus vii. 196 This and the preceding are commonly called ‘Simpson's rules’ for calculating areas; they were however previously noticed by Newton. 1909Cent. Dict. Suppl. 1158/2 Simpson's rules... In Simpson's first rule the number of ordinates is odd... Simpson's second rule. In this rule the area is divided into groups of three intervals... Simpson's 5–8 rule is used for obtaining the area of a curve between the first pair of three equally-spaced ordinates. 1930[see Runge-Kutta]. 1933L. M. Milne-Thomson Calculus of Finite Differences vii. 197 Show that Simpson's rule is tantamount to considering the curve between two consecutive odd ordinates as parabolic. 1980[see Runge-Kutta]. |