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Extension to compute the divided difference of a polynomial
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
References
- 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
See (Carlson 2010)
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- 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.
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