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SciPy Reference Guide, Release 0.8.dev
Dierckx P.
[An algorithm for surface fitting with spline functions] Ima J. Numer. Anal. 1 (1981) 267-283.
Dierckx P.
[An algorithm for surface fitting with spline functions] report tw50, Dept. Computer Science,K.U.Leuven,
1980.
Dierckx P.
[Curve and surface fitting with splines, Monographs on] Numerical Analysis, Oxford University
Press, 1993.
3.5.5 Additional tools
lagrange(x, w) Return the Lagrange interpolating polynomial of the
data-points (x,w)
approximate_taylor_polynomial(f, x, Estimate the Taylor polynomial of f at x by polynomial
degree, ...)
fitting
lagrange(x, w)
Return the Lagrange interpolating polynomial of the data-points (x,w)
Warning: This implementation is numerically unstable; do not expect to be able to use more than about 20 points
even if they are chosen optimally.
approximate_taylor_polynomial(f, x, degree, scale, order=None)
Estimate the Taylor polynomial of f at x by polynomial fitting
A polynomial Parameters ———- f : callable
x
The function whose Taylor polynomial is sought. Should accept a vector of x values.
[scalar] The point at which the polynomial is to be evaluated.
degree
[integer] The degree of the Taylor polynomial
scale
[scalar] The width of the interval to use to evaluate the Taylor polynomial. Function values spread over a
range this wide are used to fit the polynomial. Must be chosen carefully.
order
[integer or None] The order of the polynomial to be used in the fitting; f will be evaluated order+1 times.
If None, use degree.
Notes
Returns
p : poly1d
the Taylor polynomial (translated to the origin, so that for example p(0)=f(x)).
The appropriate choice of “scale” is a tradeoff - too large and the function differs from its Taylor polynomial
too much to get a good answer, too small and roundoff errors overwhelm the higher-order terms. The algorithm
used becomes numerically unstable around order 30 even under ideal circumstances.
Choosing order somewhat larger than degree may improve the higher-order terms.
210 Chapter 3. Reference