Computation of Gauss-Kronrod quadrature rules
نویسندگان
چکیده
منابع مشابه
Computation of Gauss-Kronrod quadrature rules
Recently Laurie presented a new algorithm for the computation of (2n+1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. This algorithm first determines a symmetric tridiagonal matrix of order 2n+ 1 from certain mixed moments, and then computes a partial spectral factorization. We describe a new algorithm that does not require the entries of the tridiagonal matrix to b...
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 کاملCalculation of Gauss-Kronrod quadrature rules
The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and weights can then be computed directly by standard software for Gaussian quadrature formulas.
متن کاملA Family of Gauss - Kronrod Quadrature Formulae
We show, for each n > 1, that the (2ra + l)-point Kronrod extension of the n-point Gaussian quadrature formula for the measure do-^t) = (1 + 7)2(1 t2)^2dt/((l + -y)2 47t2), -K -y < 1, has the properties that its n + 1 Kronrod nodes interlace with the n Gauss nodes and all its 2ra + 1 weights are positive. We also produce explicit formulae for the weights.
متن کاملA historical note on Gauss-Kronrod quadrature
The idea of Gauss–Kronrod quadrature, in a germinal form, is traced back to an 1894 paper of R. Skutsch. The idea of inserting n+1 nodes into an n-point Gaussian quadrature rule and choosing them and the weights of the resulting (2n+1)-point quadrature rule in such a manner as to maximize the polynomial degree of exactness is generally attributed to A.S. Kronrod [2], [3]. This is entirely justi...
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: 2000
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-00-01174-1