Dec-02-2019, 11:48 AM

Hello everyone.

I am constructing Chebyshev polinomials as specified here. I have replicated the fisrt part of the code succesfully as:

This is my code

Can someone please advice me on how to proceed to calculate the roots of a Chebyshev polynomial of order n with some guarantee of doing it well enough?

Any answer is welcome.

Regards.

I am constructing Chebyshev polinomials as specified here. I have replicated the fisrt part of the code succesfully as:

import numpy as np import sympy as sp import mpmath as mp from mpmath import * f0 = lambda x: chebyt(0,x) f1 = lambda x: chebyt(1,x) f2 = lambda x: chebyt(2,x) f3 = lambda x: chebyt(3,x) f4 = lambda x: chebyt(4,x) plot([f0,f1,f2,f3,f4],[-1,1])Now, I need to calculate the roots of said polynomials. I have found the function roots. To use it, I need to calculate the coefficients of the polynomial, that I do using the function dps as defined in the first link; the results are succesful and the coefficients are printed. However, I cannot send said output to roots.

This is my code

mp.dps = 25; mp.pretty = True for n in range(3): nprint(chop(taylor(lambda x: chebyt(n, x), 0, n))) nprint(np.roots(chop(taylor(lambda x: chebyt(n, x), 0, n))))This returns

```
Output:[1.0]
[]
[0.0, 1.0]
[]
[-1.0, 0.0, 2.0]
[ 1.41421356 -1.41421356]
```

Which means that the coefficients are propperly calculated, but np.roots doesn't return the roots. Aditionally, I have found the following thread, which indicates that roots eventually fails if the order of the polynomial reaches a high enough number.Can someone please advice me on how to proceed to calculate the roots of a Chebyshev polynomial of order n with some guarantee of doing it well enough?

Any answer is welcome.

Regards.