Thiele's interpolation formula

In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values . The problem of generating a function whose graph passes through a given set of function values is called interpolation. This interpolation formula is named after the Danish mathematician Thorvald N. Thiele. It is expressed as a continued fraction, where ρ represents the reciprocal difference:

Note that the -th level in Thiele's interpolation formula is

while the -th reciprocal difference is defined to be

.

The two terms are different and can not be cancelled!

References

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  • Weisstein, Eric W. "Thiele's Interpolation Formula". MathWorld.