Calculate roots of Chebyshev polynomials.

Calculate the roots of a Chebyshev polynomial of arbitrary degree.

Description

This function will calculate and optionally scale and translate the roots of a Chebyshev polynomial of type T_n(x) or U_n(x) of arbitrary degree.

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[John D'Errico]

Cleaned up, it works well. My tests show the correct roots. Its always nice to see the references. Both families of polynomials are now implemented in one place.

[Russell Francis]

John,

thanks for taking the time to look at and provide feedback on this relatively small and simple function. I have recently uploaded a new file which should address the 2 issues which you brought up. The function now can calculate both T_n(x) as well as U_n(x). Also the copyright notice is no longer displayed within the help inside of Matlab, which should make the function a little nicer to learn about. Please let me know if you see anything else which would improve the function.

Kind regards,
Russell Francis

[John D'Errico]

I wish the author had spent as much time documenting his code as he did in writing the extensive copyright notice, disclaimer of warranty, etc. Depressingly, more than 50% of the help section of the code is taken up by those notices.

What could he have provided that might have been useful to know? There are two distinct families of Chebyshev polynomials, yet the help refers only to a Chebyshev polynomial as if you have no choice. Take a quick read through chapter 22 of Abramowiz and Stegun. Which kind is this? (Hint: T_n)

Even better, provide a flag that lets the user decide which polynomial family they will get. Yes, this might double the size of the code, but only a single set of disclaimers and copyright notices would be "needed".