On computing Gauss-Kronrod quadrature formulae
نویسندگان
چکیده
منابع مشابه
A 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.
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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...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1986-0856708-8