منابع مشابه
On generalized averaged Gaussian formulas
We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x) ≡ w(α,β)(x) = (1− x)α(1 + x)β (α, β > −1) we give a necessary and sufficient ...
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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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We present a formula for computing proper pushforwards of classes in the Chow ring of a projective bundle under the projection π : P(E )→ B, for B a non-singular compact complex algebraic variety of any dimension. Our formula readily produces generalizations of formulas derived by Sethi,Vafa, and Witten to compute the Euler characteristic of elliptically fibered Calabi-Yau fourfolds used for F-...
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1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...
متن کاملGeneralized averaged Szegő quadrature rules
Szegő quadrature rules are commonly applied to integrate periodic functions on the unit circle in the complex plane. However, often it is difficult to determine the quadrature error. Recently, Spalević introduced generalized averaged Gauss quadrature rules for estimating the quadrature error obtained when applying Gauss quadrature over an interval on the real axis. We describe analogous quadrat...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-01975-8