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Thiele's interpolation formula: Difference between revisions
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Now the recursive relation is simply
:<math>\rho_{n,i} = \displaystyle{x_i - x_{i + n} \over \rho_{n-1,i} - \rho_{n-1,i+1}} + \rho_{n-2,i+1}, \ 0\leq i+n \leq N</math>
Also note how <math>f(x_1)</math> in the interpolation formula can be replaced by <math>\rho_{0,1}</math>; define Thiele interpolation at step <math>n</math> as
:<math>\displaystyle{F_n(x) = \rho_{n,1} - \rho_{n - 2, 1} + { x - x_{n+1}\over F_{n+1}(x)}}</math>
with the termination <math>F_N(x) = 1</math>, and the interpolation formula is now <math>f(x) = F_0(x)</math>, easily implemented as a recursive function.
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