There are articles on curve fitting and polynomial interpolation and others plus lots of packages to do it, but saying one interpolation is better than another is a difficult thing . talk ) 14 : 51, 15 June 2010 ( UTC)
32.
When, with Stirling's or Bessel's, the last term used includes the average of two differences, then one more point is being used than Newton's or other polynomial interpolations would use for the same polynomial degree.
33.
The first generation Privia was produced from 2003 to 2006, and utilizes the "'Zygotech Polynomial Interpolation "'( "'ZPI "') synthesis sound engine, as used in Casio's numerous former flagship keyboards.
34.
While a polynomial interpolation or extrapolation only yields good results if the nearest pole is rather far outside a circle around the known data points in the complex plane, rational function interpolation or extrapolation can have remarkable accuracy even in the presence of nearby poles.
35.
If a " C " 0 function is insufficient, for example if the process that has produced the data points is known be smoother than " C " 0, it is common to replace linear interpolation with spline interpolation or, in some cases, polynomial interpolation.
36.
:: : My quick search didn't turn up specifics on the kind of interpolation ( other than the phrase " simple interpolation method " ), but this page shows an example Robinson map with a caption saying " . . . calculated with 3rd degree polynomial interpolation ", for what it is worth.
37.
So, in that instance, Stirling's or Bessel's is not putting an " N " " 1 degree polynomial through " N " points, but is, instead, trading equivalence with Newton's for better centering and accuracy, giving those methods sometimes potentially greater accuracy, for a given polynomial degree, than other polynomial interpolations.
38.
Another possible way of calculating e ( x ) is using polynomial interpolation to find the only polynomial that passes through the points ( \ alpha ^ j, S _ j ) ( Because S _ j = e ( \ alpha ^ j ) ), however, this is not used widely because polynomial interpolation is not always feasible in the fields used in Reed Solomon error correction.
39.
Another possible way of calculating e ( x ) is using polynomial interpolation to find the only polynomial that passes through the points ( \ alpha ^ j, S _ j ) ( Because S _ j = e ( \ alpha ^ j ) ), however, this is not used widely because polynomial interpolation is not always feasible in the fields used in Reed Solomon error correction.
