A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(logN)2/ log logN) operations is derived. The basis of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the di...

Through a geometncal approach of the blossoming pnnciple, we achieve a dimension élévation process for extended Chebyshev spaces Applied to a nested séquence ofsuch spaces included in a polynomial one, this allows to compute the Bézier points from the initial Chebyshev-Bézier points This method leads to interesting shape effects © Elsevier, Paris

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

a0Tn(x) + a1Tn−1(x) + · · ·+ amTn−m(x) where (a0, a1, . . . , am) is a fixed m-tuple of real numbers, a0, am 6= 0, Ti(x) are Chebyshev polynomials of the first kind, n = m, m + 1, m + 2, . . . Here we analyze the structure of the set of zeros of such polynomial, depending on A and its limit points when n tends to infinity. Also the expression of envelope of the polynomial is given. An applicati...