Uniqueness of the Gaussian interval quadrature formula

Uniqueness and computation of Gaussian interval quadrature formula for Jacobi weight function

“…For the (i) part, the proof is exactly the same as it is given in [2]. Actually, the same proof suffices to prove the previous lemma for any strictly positive weight function w(x) = dµ/dx on (−1, 1), which does not take zero as its value.…”

“…[7]). Only recently in [1] and [2], quadrature rules involving integrals of a function on some parts of supp(µ) have been investigated, i.e., quadrature rules of the form…”

“…In [2], it was proved that for the Legendre measure, i.e., w(x) = 1, and any set of lengths h k ≥ 0, k = 1, . .…”

Gauss-Radau and Gauss-Lobatto interval quadrature rules for Jacobi weight function

“…The rest of the proof goes exactly as it is given in [3]. The proof has N steps, where N is defined by h = (N + η) ε 0 4 , 0 < η ≤ 1, with h = max{h 0 , .…”

“…In [2], Bojanov Evidently, the existence of the Gaussian interval quadrature formula (1.1) follows directly from this general result. In [3], it was proved that for the weight w(x) = 1 on [−1, 1], the Gaussian interval quadrature rule is also unique, and in [7] the same result was proved for the Jacobi weight function on [−1, 1].…”