“Newton’s interpolating polynomial”的概念、定义、翻译、参考文献-科学参考

Newton’s interpolating polynomial

Mathematics

The polynomial of degree n, which interpolates n + 1 evenly spaced data points (x₀,y₀), (x₁,y₁),…, (x_n,y_n), where x_k = x₀ + kh, is given by

$y_{0} + \frac{(x - x_{0})}{h} ∆ y_{0} + \frac{(x - x_{0}) (x - x_{1})}{2! h^{2}} ∆^{2} y_{0} + \dots + \frac{(x - x_{0}) \dots (x - x_{n})}{n! h^{n}} ∆^{n} y_{0}$

where $∆ y_{0} = y_{1} - y_{0}$ , $∆^{2} y_{0} = ∆ y_{1} - ∆ y_{0}$ , etc. which are obtained by constructing a forward difference table.

单词	Newton’s interpolating polynomial
释义	Newton’s interpolating polynomial Mathematics The polynomial of degree n, which interpolates n + 1 evenly spaced data points (x₀,y₀), (x₁,y₁),…, (x_n,y_n), where x_k = x₀ + kh, is given by $y_{0} + \frac{(x - x_{0})}{h} ∆ y_{0} + \frac{(x - x_{0}) (x - x_{1})}{2! h^{2}} ∆^{2} y_{0} + \dots + \frac{(x - x_{0}) \dots (x - x_{n})}{n! h^{n}} ∆^{n} y_{0}$ where $∆ y_{0} = y_{1} - y_{0}$ , $∆^{2} y_{0} = ∆ y_{1} - ∆ y_{0}$ , etc. which are obtained by constructing a forward difference table.
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