For such a function, a smooth quadratic interpolant like the one used in Simpson's rule will give good results.
12.
And changing the points x _ j requires recalculating the entire interpolant, so it is often easier to use Newton polynomials instead.
13.
This inequality also follows from the well-known error estimate for linear interpolation by choosing \ textstyle v as the linear interpolant of \ textstyle u.
14.
It is clear that ( a ) and ( b ) imply that there is a small interpolant circuit, which is in contradiction with ( c ).
15.
The interpolant circuit decides either if A ( x, y ) is false or if B ( y, z ) is true, by only considering y.
16.
The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant.
17.
It is possible to include more than two points, and averaging the slope of the linear interpolant, by regression-like techniques, on the data points chosen to be included.
18.
However, these maxima and minima may exceed the theoretical range of the function for example, a function that is always positive may have an interpolant with negative values, and whose inverse therefore contains false vertical asymptotes.
19.
As an interpolant, the coefficients of the th partial sum are usually obtained on the Chebyshev Gauss Lobatto points ( or Lobatto grid ), which results in minimum error and avoids Runge's phenomenon associated with a uniform grid.
20.
Some proof systems ( e . g . resolution ) are said to have " efficient interpolation " because the interpolant C ( y ) is efficiently computable from any proof of the tautology A ( x, y ) \ rightarrow B ( y, z ) in such proof system.
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