Quadrature formulae of Gauss type based on Euler identities
نویسندگان
چکیده
منابع مشابه
A Survey of Gauss-Christoffel Quadrature Formulae
4. 4.1. 4.1.1. 4.1.2. 4.1.3. 4.2. 4.3. Gaussian quadrature with preassigned nodes Christoffel's work and related developments Kronrod's extension of quadrature rules Gaussian quadrature with multiple nodes The quadrature formula of Turan Arbitrary multiplicities and preassigned nodes Power-orthogonal polynomials Constructive aspects and applications Further miscellaneous extensions Product-type...
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 کاملError Bounds for Gauss-kronrod Quadrature Formulae
The Gauss-Kronrod quadrature formula Qi//+X is used for a practical estimate of the error R^j of an approximate integration using the Gaussian quadrature formula Q% . Studying an often-used theoretical quality measure, for ߣ* , we prove best presently known bounds for the error constants cs(RTMx)= sup \RlK+x[f]\ ll/(l»lloo<l in the case s = "Sn + 2 + tc , k = L^J LfJ • A comparison with the Ga...
متن کاملError bounds for Gauss-Tur'an quadrature formulae of analytic functions
We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑
متن کاملGauss-chebyshev Quadrature Formulae for Strongly Singular Integrals
This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. T...
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: Mathematical and Computer Modelling
سال: 2007
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2006.05.009