Chebyshev Polynomials - Application to Polynomial Interpolation
Contents
Finding Roots of a Chebyshev Polynomial
For a given value between -1 and 1, the solutions to are , where ranges from 1 to and .
For each of these values, we have
Since we have solutions to a degree polynomial, these are all of the roots.
In terms of , what are the roots of
In terms of , what are the roots of
In terms of , what are the roots of
Finding Minimal Polynomial of Roots in Trigonometric Form
The converse of the above theorem is as follows:
The polynomial whose roots are , where ranges from 1 to , is
In terms of , find a polynomial whose roots are .
In terms of , find a polynomial whose roots are for to
Additional Questions
To answer problems in this section, you should be familiar with Vieta's formula to help you find the sum and product of roots.
Evaluate
Evaluate
In terms of , find a polynomial whose roots are exactly