On the computation of the Gauss–Legendre quadrature formula with a given precision

摘要

The paper is concerned with error bounds for iterative methods for the numerical approximation of the zeros xν of Legendre polynomials, i.e., the nodes of the Gauss–Legendre quadrature formula QnG. From these bounds, new stopping criteria are derived. It is furthermore shown, how the calculation of the weights of QnG may depend on the precision of the approximation of xν.