when you derive an interpolating polynomial say through 3 points is there a chance for that polynomial to satisfy any other point other than those 3 points? (Any other point in the same domain)
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Welcome to MSE! Try using mathjax to make you question more presentable. – For the love of maths Dec 28 '17 at 17:03
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Yes, it's possible. Think, for example, of interpolating three points on a parabola with a second-order polynomial. – Fabio Somenzi Dec 28 '17 at 17:10
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Then is there any other way to express a relationship between those 3 points which is not satisfied by any other point? – Buddhini Angelika Dec 28 '17 at 17:19
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There's the obvious solution of specifyingthe set of those three points, e.g., ${(x_1,y_1),(x_2,y_2),(x_3,y_3)}$. But I suspect there are some additional conditions that you have in mind. – Fabio Somenzi Dec 28 '17 at 17:29