Order of approximation: Difference between revisions

Revision as of 05:48, 16 March 2023

Revision as of 05:48, 16 March 2023

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One should be careful though, because the multiplicative function will be defined for the whole interval. If only three data points are available, one has no knowledge about the rest of the [[Interval (mathematics)|interval]], which may be a large part of it. This means that ''y'' could have another component which equals 0 at the ends and in the middle of the interval. A number of functions having this property are known, for example ''y'' = sin π''x''. [[Taylor series]] is useful and helps predict an [[Closed-form expression|analytic solution]], but the approximation alone does not provide conclusive evidence.

===Higher-order===

While higher-order approximations exist and are crucial to a better understanding and description of reality, they are not typically referred to by number.

Continuing the above, a third-order approximation would be required to perfectly fit four data points, and so on. See [[polynomial interpolation]].

==Colloquial usage==