Abstract:
This study is concerned with Chebyshev polynomials and their applications in numerical computation. The basic properties of the first kind Chebyshev polynomials in the interval [-1, 1], are used extensively. Three different applications of the first kind Chebyshev polynomials are studied. First, a sufficient condition for convergence of Chebyshev semi-iterative methods applied to the numerical solution of algebraic linear systems is proved. The convergence condition depends on the bounds on the eigenvalues of a square matrix. Second, the problem of approximating a given function by Chebyshev polynomials is considered. The approximating polynomials are used to predict the value of the function at Chebyshev zeros “roots”. Third, the Gauss - Chebyshev quadrature method for the numerical integration of a given function over a finite range is applied. It consists essentially of expanding the integral in a series of Chebyshev polynomials.
