FunctionApproximations`
FunctionApproximations`

# GeneralMiniMaxApproximation

GeneralMiniMaxApproximation[{fx,fy},{t,{t0,t1},m,n},x]

finds the rational polynomial function of x, with numerator order m and denominator order n, that gives a mini-max approximation to the curve with x and y coordinates fx and fy generated as a function of t on the interval t0 to t1.

GeneralMiniMaxApproximation[{fx,fy},approx,{t,{t0,t1},m,n},x]

finds the mini-max approximation, starting the iterative algorithm with approx.

# Details

• To use GeneralMiniMaxApproximation, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
• GeneralMiniMaxApproximation by default minimizes the maximum value of the relative error between the approximation and expr.
• GeneralMiniMaxApproximation[{fx,fy,g},{t,{t0,t1},m,n},x] computes the error using a factor of g. In this case the mini-max approximation returned by GeneralMiniMaxApproximation is the rational function h[x] that minimizes the maximum value of the quantity (fy-h[fx])/g.
• GeneralMiniMaxApproximation returns {abscissa,{approximation,maxerror}}, where abscissa is a list of the abscissas where the relative error is a local maximum, approximation is the rational approximant, and maxerror is the global maximum of the relative error.
• When an approximation is given as the second argument of GeneralMiniMaxApproximation, it must have the same form as the result returned by GeneralMiniMaxApproximation.
• The following options can be given:
•  Bias 0 bias in the automatic choice of interpolation points Brake {5,5} braking to apply on iterative algorithm Derivatives Automatic function to use for derivatives MaxIterations 20 maximum number of iterations to use PlotFlag False whether to plot relative error PrintFlag False whether to print status information WorkingPrecision MachinePrecision precision to use in internal computations