Roots of the Chebyshev polynomials
The roots of are . These will be the nodes for polynomial approximation of degree n.
Exploration 3.
(c) John H. Mathews 2004
![[Graphics:Images/ChebyshevPolyMod_gr_89.gif]](../Images/ChebyshevPolyMod_gr_89.gif){kind=small}
are ![[Graphics:Images/ChebyshevPolyMod_gr_90.gif]](../Images/ChebyshevPolyMod_gr_90.gif){kind=small}
. These
will be the nodes for polynomial approximation of degree
n. are . These
will be the nodes for polynomial approximation of degree
n. ![[Graphics:../Images/ChebyshevPolyMod_gr_91.gif]](../Images/ChebyshevPolyMod_gr_91.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_92.gif]](../Images/ChebyshevPolyMod_gr_92.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_93.gif]](../Images/ChebyshevPolyMod_gr_93.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_94.gif]](../Images/ChebyshevPolyMod_gr_94.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_95.gif]](../Images/ChebyshevPolyMod_gr_95.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_96.gif]](../Images/ChebyshevPolyMod_gr_96.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_97.gif]](../Images/ChebyshevPolyMod_gr_97.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_98.gif]](../Images/ChebyshevPolyMod_gr_98.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_99.gif]](../Images/ChebyshevPolyMod_gr_99.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_100.gif]](../Images/ChebyshevPolyMod_gr_100.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_101.gif]](../Images/ChebyshevPolyMod_gr_101.gif)
![[Graphics:../Images/ChebyshevPolyMod_gr_102.gif]](../Images/ChebyshevPolyMod_gr_102.gif){kind=small}
![[Graphics:../Images/ChebyshevPolyMod_gr_103.gif]](../Images/ChebyshevPolyMod_gr_103.gif)