We discuss the use of Newton's method for computing Gauss-Kronrod quadrature formulae from modified moments. The underlying nonlinear maps are analyzed from the point of view of numerical condition. A ...

Quadrature rules are mathematical techniques used to approximate the definite integral of a function. They are essential in numerical analysis and scientific computing, particularly when dealing with ...

Abstract. It is well-known that the remaining term of any 𝑛-point interpolatory quadrature rule such as Gauss-Legendre quadrature formula depends on at least an 𝑛-order derivative of the integrand ...