Extension to compute the divided difference of a polynomial

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Horner's method can be modified to compute the dividing difference,  . Given the polynomial (as before)

 

proceed as follows[1]

 

At completion, we have   and  . This computation of the divided difference is subject to much less round-off error than evaluating   and   separately, particularly when  . Substituting   in this method gives  , the derivative of  .

Notes

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References

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  • Fateman, R. J.; Kahan, W. (2000). Improving exact integrals from symbolic algebra systems (PDF) (Report). PAM. University of California, Berkeley: Center for Pure and Applied Mathematics.

Misc

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/Theoretical Gravity

See (Carlson 2010)

This is the English translation of Bessel, F. W. (1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen". Astronomische Nachrichten. 4 (16): 241–254. arXiv:0908.1823. Bibcode:1825AN......4..241B. doi:10.1002/asna.18260041601.