Lobatto-type quadrature formula in rational spaces

This paper constructs the Lobatto-type quadrature formula for the rational space R2n−1(a1,…,an):=P(x)Πnk=1z.sfnc;x−ak|2,Pϵp2n−1 with the nonreal elements in {ak}k = 1n ⊂ Cβ[−1,1] paired by complex conjugation. This Lobatto-type quadrature formula is based on the extreme points of the Chebyshev polynomial of the first kind with the rational space Pn(a1,…,an). Moreover, it is exact for any element in R2n − 1(a1,…,an).