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# Polynomial used in Interpolation

Posted 10 years ago
 Dear friends,How could I get the polynomial used in the Interpolation command? What is, for example, the polynomial used in the following interpolation:data = Table[{i, RandomReal[i]}, {i, 1, 10}];f = Interpolation[data];What was the order used in the "f = Interpolation[ data]"?Thanks,Ana
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Posted 10 years ago
 Thank you for all
Posted 10 years ago
 data = Table[{i, RandomReal[i]}, {i, 1, 10}];InterpolatingPolynomial[data, x] // ExpandOut[] = 1227.24 - 3354.85 x + 3658.58 x^2 - 2130.21 x^3 + 740.403 x^4 -         161.038 x^5 + 22.1034 x^6 - 1.8587 x^7 + 0.0873782 x^8 - 0.0017578 x^9
Posted 10 years ago
 The default method is "Hermite" See how-does-interpolation-really-workIf you want to force a polynomial to be used, you can use the Fit command. (but not a good idea to use polynominal to fit  many points, else too much oscillation in between points, see Runge's phenomenon) that is why Spline or Hermite would be better methods.