Evaluates the coefficients of the interpolating polynomial when the tabulation points are known.
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.An array of double where the i-th term is the i-th coefficient within the interpolation function.
Further Explanation
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.
Comparison with CoefficientsInterpolatingPolynomial
The method CoefficientsInterpolatingPolynomial differs slightly from this method which is less direct and slower by a power of the number of tabulation points used. However, we have found this approach to be more stable. The essential idea in this approach is that it uses the InterpolateExtrapolatePolynomial 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 . |
Interpolation Class | WebCab.COM.Finance.Portfolio Namespace | CoefficientsInterpolatingPolynomial | InterpolateExtrapolatePolynomial