  Chebyshev polynomials of the first and second kind for a set K are monic
polynomials with minimal L $\infty$-and L 1-norm on K, respectively. This
articles presents numerical procedures based on semidefinite programming to
compute these polynomials in case K is a finite union of compact intervals. For
Chebyshev polynomials of the first kind, the procedure makes use of a
characterization of polynomial nonnegativity. It can incorporate additional
constraints, e.g. that all the roots of the polynomial lie in K. For Chebyshev
polynomials of the second kind, the procedure exploits the method of moments.
Key words and phrases: Chebyshev polynomials of the first kind, Chebyshev
polynomials of the second kind, nonnegative polynomials, method of moments,
semidefinite programming.
