2-04-08 - Interpolation Discreteanalysis o Goal: o...

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2/4/08 Interpolation Discrete analysis o Goal: Find continuous functions from discrete data o Linear interpolation Let x i < x < x i+1 Know y i =f(x i ) y i +1 = f(x i +1) Question: y=f(x)? y = y i + (y i +1 – yi) ((x‐x i )/(x i +1‐x i )) =f(x) Nonlinear interpolation Polynomial interpolation General n th order polynomial P n (x) = a 0 +a 1 x+a 2 x 2 + +a n x n all a i (n+1 of them) are unknown constants
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