Functions > Data Analysis > Interpolation and Prediction > Thiele Continued Fraction Interpolation
Thiele Continued Fraction Interpolation
Thielecoeff(vx, vy)—Returns the continued fraction coefficients of the vectors vx and vy.
You can use the Thiele coefficients to generate a polynomial expression that fits the data. This should be done with caution as the conversion process and the resulting polynomial evaluation may have roundoff error issues.
Thiele(vx, coeff, x)—Returns the interpolated y value for the real scalar x, using the data points in vx and the coefficients coeff returned by Thielecoeff.
The Theile function performs interpolation at a requested point, x, using continued-fraction approximations between points. Use this function to evaluate the continued fraction expansion. This type of interpolation is useful for data with asymptotes or of a rational polynomial form that result in a failure of other types of rational polynomial interpolation.
The Thiele function is based on work in Hildebrand, F.B. (1974), Introduction to Numerical Analysis, 2nd Ed., McGraw Hill.
Arguments
vx, vy are real vectors of data values of the same length.
coeff is a vector of continued fraction coefficients returned by the Thielecoeff function.
x is the value of the independent variable at which you want to evaluate the interpolation curve. For best results, x should be in the range encompassed by the values of vx.