I am making a program to find a polynomial given a set of data. I understand the summation of the formula. Given the image below can someone explain what the square looking symbol is next to the Li(x)? Can you explain the Li(x) function to me as well?
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Do you mean the $\Pi$ symbol? That's a product symbol. – littleO Nov 19 '18 at 23:13
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Yes, and ok can you explain how to use Li(x). I don't understand. So for every x value, we are given we calculate Li for all the x values? – User Nov 19 '18 at 23:17
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$L_i(x)$ sends $x_i$ to 1 and all other $x_j$ to 0. Thus summing up $y_i L_i(x)$ over $i$ gives an interpolant of all of the $(x_i,y_i)$. – Ian Nov 19 '18 at 23:20
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So for Li(x) we calculate the product of the formula for each j in J but we skip over the i-th element – User Nov 19 '18 at 23:25
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That is correct. This is needed so that $L_i(x_i)$ is nonzero. – Ian Nov 20 '18 at 02:13
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Perhaps you can understand it via this example on 3 points. This Desmos graph is interactive and you can create any interpolation on 3 points with it.
Calvin Khor
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