“Gregory–Newton forward difference formula”的概念、定义、习题解题方法及翻译-数学辞典

单词

Gregory–Newton forward difference formula

释义

Gregory–Newton forward difference formula

Let x0, x1, x2,…, xn be equally spaced values, so that xi = x0 + ih, for i = 1, 2,…, n. Suppose that the values f0, f1, f2,…, fn are known, where fi = f(xi), for some function f. The Gregory–Newton forward difference formula is a formula involving finite differences that gives an approximation for f(x), where x = x0 + θh, and 0<θ<1. It states that

the series terminating at some stage. The approximation f(x) ≈ f0 + θΔ f0 gives the result of linear interpolation. Terminating the series after one more term provides an example of quadratic interpolation.

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