Newton,s Divided Difference Interpolation Formula
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover,
الجزء والصفحة:
...
21-11-2021
1842
Newton's Divided Difference Interpolation Formula
Let
 |
(1)
|
then
![f(x)=f_0+sum_(k=1)^npi_(k-1)(x)[x_0,x_1,...,x_k]+R_n,](https://mathworld.wolfram.com/images/equations/NewtonsDividedDifferenceInterpolationFormula/NumberedEquation2.gif) |
(2)
|
where ![[x_1,...]](https://mathworld.wolfram.com/images/equations/NewtonsDividedDifferenceInterpolationFormula/Inline1.gif)
is a divided difference, and the remainder is
![R_n(x)=pi_n(x)[x_0,...,x_n,x]=pi_n(x)(f^((n+1))(xi))/((n+1)!)](https://mathworld.wolfram.com/images/equations/NewtonsDividedDifferenceInterpolationFormula/NumberedEquation3.gif) |
(3)
|
for 
.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 880, 1972.
Hildebrand, F. B. Introduction to Numerical Analysis. New York: McGraw-Hill, pp. 43-44 and 62-63, 1956.
Whittaker, E. T. and Robinson, G. "Newton's Formula for Unequal Intervals." §13 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 24-26, 1967.
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