FunctionApproximations`
FunctionApproximations`
EconomizedRationalApproximation
EconomizedRationalApproximation[expr,{x,{x0,x1},m,n}]
gives the economized rational approximation to expr that is good over the interval x0 to x1, with numerator order m and denominator order n.
Details and Options
- To use EconomizedRationalApproximation, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
- EconomizedRationalApproximation finds the Padé approximant about the midpoint of the interval x0 to x1, and then perturbs the approximant with Chebyshev polynomials to reduce the leading coefficient in the error.
- The Wolfram Language can find the economized rational approximant over the interval x0 to x1 only when it can evaluate power series at the midpoint of the interval.
- EconomizedRationalApproximation produces a ratio of ordinary polynomial expressions, not a special SeriesData object.