compute Thiele's continued fraction interpolating function - Maple Help

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CurveFitting[ThieleInterpolation] - compute Thiele's continued fraction interpolating function

Calling Sequence

ThieleInterpolation(xydata, v)

ThieleInterpolation(xdata, ydata, v)




list, Array, or Matrix of the form [[x1,y1], [x2,y2], ..., [xn,yn]]; data points



list, Array, or Vector of the form [x1, x2, ..., xn]; independent values



list, Array, or Vector of the form [y1, y2, ..., yn]; dependent values



name or numeric value



The ThieleInterpolation routine returns the rational function in continued fraction form in variable v that interpolates the points {x1,y1,x2,y2,...,xn,yn}.  If v is a numerical value, then the value of the function at this point is returned.  When n is odd, the numerator and denominator polynomials have degree 12n12.  When n is even, the numerator has degree 12n and the denominator has degree 12n1.


The ThieleInterpolation routine can be called in two ways.


The first form accepts a list, Array, or Matrix, [[x1,y1],[x2,y2],...,[xn,yn]], of data points.


The second form accepts the input data as two lists, two Arrays, or two Vectors. In this form, the first set of data contains the independent values, [x1,x2,...,xn], and the second set of data contains the dependent values, [y1,y2,...,yn].  Each element must be of type algebraic.  All the independent values must be distinct.


In certain situations, the algorithm for computing the Thiele interpolating function produces a denominator of zero.  For example, a division-by-zero error is produced when two successive points have the same dependent value or when three successive points are collinear.  In such cases, perturbing the data points slightly may eliminate the problem.


This function is part of the CurveFitting package, and so it can be used in the form ThieleInterpolation(..) only after executing the command with(CurveFitting).  However, it can always be accessed through the long form of the command by using CurveFitting[ThieleInterpolation](..).









See Also

CurveFitting, type/algebraic

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