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.