Answer to Question #94290 in Quantitative Methods for Dorcas

Question #94290
The interpolating polynomial of degree \\(\\leq n\\)with the nodes\\(x_{0}, x_{1},\\cdots, x_{n}\\) can be written as
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Expert's answer
2019-09-12T09:12:37-0400

p(x)=anxn+an1xn1++a2x2+a1x+a0,p(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_2x^2 + a_1x + a_0, \\

where p(xi)=yi for all i{0,1,,n}p(x_i) = y_i \text{ for all } i \in \{ 0,1,\dots,n \}.


Lagrange polynomial: p(x)=i=0n(0jn;jixxjxixj)yip(x) = \sum_{i=0}^n ( \prod_{0 \leq j \leq n; j \not= i} \frac{x-x_j}{x_i-x_j} ) y_i


More detailed info: https://en.wikipedia.org/wiki/Polynomial_interpolation


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