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:

Be careful 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

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


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.