Reciprocal difference


Reciprocal difference

In mathematics, the reciprocal difference of a finite sequence of numbers (x_0, x_1, ..., x_n) on a function f(x) is defined inductively by the following formulas:

: ho_1(x_0, x_1) = frac{x_0 - x_1}{f(x_0) - f(x_1)}

: ho_2(x_0, x_1, x_2) = frac{x_0 - x_2}{ ho_1(x_0, x_1) - ho_1(x_1, x_2)} + f(x_1)

: ho_n(x_0,x_1,ldots,x_n)=frac{x_0-x_n}{ ho_{n-1}(x_0,x_1,ldots,x_{n-1})- ho_{n-1}(x_1,x_2,ldots,x_n)}+ ho_{n-2}(x_1,ldots,x_{n-1})

ee also

*divided differences

References

*MathWorld|title=Reciprocal Difference|urlname=ReciprocalDifference
*citebook|last=Abramowitz|first=Milton|coathor=Irene A. Stegun|title=Handbook of Mathematical Functions|origyear=1964|year=1972|publisher=Dover|edition=ninth Dover printing, tenth GPO printing|pages=878|id=ISBN 0-486-61272-4


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