Positivity of the weights of extended Gauss-Legendre quadrature rules
نویسندگان
چکیده
منابع مشابه
Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules
We show that the weights of extended Gauss-Legendre quadrature rules are all positive.
متن کاملGauss Legendre-Gauss Jacobi quadrature rules over a tetrahedral region
This paper presents a Gaussian quadrature method for the evaluation of the triple integral ( , , ) T I f x y z d xd yd z = ∫∫∫ , where ) , , ( z y x f is an analytic function in , , x y z and T refers to the standard tetrahedral region:{( , , ) 0 , , 1, 1} x y z x y z x y z ≤ ≤ + + ≤ in three space( , , ). x y z Mathematical transformation from ( , , ) x y z space to ( , , ) u v w space maps th...
متن کاملIteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights
Gauss–Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss–Legendre weights is derived. Together, these two expansions provide a practical ...
متن کاملFast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights
An efficient algorithm for the accurate computation of Gauss–Legendre and Gauss– Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton’s root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100.
متن کاملComputation of Gauss-kronrod Quadrature Rules with Non-positive Weights
Recently Laurie presented a fast algorithm for the computation of (2n + 1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of Gauss-Kronrod quadrature rules with complex conjugate nodes and weights or with real nodes and positive and negative weights.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0458809-0