Evaluates the coefficients of the interpolating polynomial in 1 variable when the polynomial is known as a set of tabulation points.
f' is the interpolating polynomial then we have f(tabulatedValues[i]) = polynomialValues[i]; where `polynomialValues[i]' is the value of the interpolating polynomial at the `tabulatedValues[i]'.polynomialValues[0]', corresponds to the value of the interpolating polynomial at the first tabulation point `tabulatedValues[0]', and the second values `polynomialValues[1]' corresponds to the value of the interpolating polynomial at the second tabulated point `tabulatedValues[1]', and so on.This methods is a slower but more stable version of CoefficientsInterpolatingPolynomial. That is, a set of points in the range and the corresponding values in the domain of the interpolation function are known and we will deduce from this information the coefficients of the corresponding interpolation polynomial assuming the degree of this polynomial is one less than the number of tabulation points used.
If we are given a set of n points on which the interpolation function
is known then this method evaluates the n coefficients c_i
of the interpolation function c_0 + (c_1 * x) + (c_2 * x * x)+ ....
More explicitly, given a set of tabulation points x = {x[i]: i=0,...,n-1}
and y = {y[i]:i=0,...,n-1}
which defines a function by y[i] = f(x[i]). This method returns an array of
doubles which are the coefficients of the interpolating polynomial where the first term
of the array corresponds to the 0th order term, the second term corresponds to the 1st order
term (i.e. x's coefficient) and so on.
The method CoefficientsInterpolatingPolynomial differs slightly from this method which is less direct and slower by a power of the number of points used. However, we have found this approach to be more stable. The essential idea in this approach is that it uses the InterPoly method with iterative reduction to arrive at the interpolation polynomial.
Remark: If the two arrays have different lengths the shorter one will be used as reference.
| Exception Type | Condition |
|---|---|
| InterpolationException | Thrown when any of the two parameters are null. |
Inter Class | Interpolation Namespace | CoefficientsInterpolatingPolynomial | InterPoly