Interpolation筆記

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###證明筆記,如有空再補上說明###

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1. 線性內插(Linear Interpolation)

$ y = ax + b , f(x) = ax + b $

$ y_i = a x_i + b $

$ y_{i+1} = a x_{i+1} + b $

$ y_{i+1} - y_i = a_{i+1} -a x_i $

$ y_{i+1} - y_i = a (x_{i+1} -a x_i) $

$ y_{i+1} - y_i/(x_{i+1} -x_i) = a $

$ y_i = (y_{i+1} - y_i/(x_{i+1} -x_i))x_i + b $

$ y_i - ax_i = b $

$ f(x) = (y_{i+1} - yi/(x_{i+1} -x_i))x + yi -ax_i $

$ f(x) = (y_{i+1} - yi/(x_{i+1} -xi))(x-xi) + yi $