منابع مشابه
Anti-Gaussian quadrature formulas
An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...
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Gaussian formulas are among the most often used quadrature formulas in practice. In this survey, an overview is given on stopping functionals for Gaussian formulas which are of the same type as quadrature formulas, i.e., linear combinations of function evaluations. In particular, methods based on extended formulas like the important Gauss-Kronrod and Patterson schemes, and methods which are bas...
متن کاملNumerical Construction of Gaussian Quadrature Formulas for
Most nonclassical Gaussian quadrature rules are difficult to construct because of the loss of significant digits during the generation of the associated orthogonal polynomials. But, in some particular cases, it is possible to develop stable algorithms. This is true for at least two well-known integrals, namely ¡l-(Loêx)-x°f(x)dx and ¡Ô Em(x)f(x)-dx. A new approach is presented, which makes use ...
متن کاملConstruction of σ-orthogonal Polynomials and Gaussian Quadrature Formulas
Let dα be a measure on R and let σ = (m1,m2, ..., mn), where mk ≥ 1, k = 1, 2, ..., n, are arbitrary real numbers. A polynomial ωn(x) := (x − x1)(x − x2)...(x − xn) with x1 ≤ x2 ≤ ... ≤ xn is said to be the n-th σ-orthogonal polynomial with respect to dα if the vector of zeros (x1, x2, ..., xn) is a solution of the extremal problem ∫
متن کاملComposite Hermite - Birkhoff Quadrature Formulas of Gaussian Type
We show how to combine incidence matrices, which admit Hermite-Birkhoff quadrature formulas of Gaussian type for any positive measure, in such a way that the resulting matrix also admits Gaussian type quadratures for any positive measure. Moreover, the uniqueness property and the extremal property of the formulas corresponding to the submatrices are transferred to the formula admitted by the co...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1996
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-96-00713-2