*PM : lecture notes on polynomial interpolation, id = 9116 new !-- WP guess : lecture notes on polynomial interpolation-- Status:
22.
We conclude again that Chebyshev nodes are a very good choice for polynomial interpolation, as the growth in " n " is exponential for equidistant nodes.
23.
Chebyshev polynomials are important in approximation theory because the roots of the Chebyshev polynomials of the first kind, which are also called Chebyshev nodes, are used as nodes in polynomial interpolation.
24.
So, Bessel's formula could be said to be the most consistently accurate difference formula, and, in general, the most consistently accurate of the familiar polynomial interpolation formulas.
25.
In interpolation problems, " spline interpolation " is often preferred to polynomial interpolation because it yields similar results to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon.
26.
I could use polynomial interpolation on the first k + 2 terms of the series, but that gets impractical quickly if k is large . talk ) 21 : 47, 25 November 2016 ( UTC)
27.
Polynomial interpolation is also essential to perform sub-quadratic multiplication and squaring such as Karatsuba multiplication and Toom Cook multiplication, where an interpolation through points on a polynomial which defines the product yields the product itself.
28.
Then it uses polynomial interpolation to recover the unique univariate polynomial h with degree less than or equal to d such that h ( \ lambda ) = e _ { \ lambda } for all \ lambda \ in S.
29.
Complicated functions are also sometimes approximated using polynomial interpolation, although care needs to be taken sometimes ( using a high order polynomial to approximate the path your Mars lander needs to take may result in one that dips below ground level ).
30.
So, you can act as if you wanted to get some values between them-in such case polynomial interpolation would give you exact fit in those 999 points ( that is, if we could somehow avoid the rounding errors ).
