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Inversely Symmetric Interpolatory Quadrature Rules

Acta Applicandae Mathematica, 2000
Let \(d\phi (x)\) a symmetric distribution defined on \([-d,d]\), with \(d>0\). Further, let \(d\psi (t)\) be a strong weight distribution defined on \((\beta^2/b,b)\), where \(0< \beta< b\leq \infty\), and such that \[ d\psi (t)/\sqrt t=-d\psi (\beta ^2/t)/\sqrt {\beta ^2/t}. \] The authors consider the transformation \(x(t)=1/(2\sqrt \alpha)(\sqrt t -
De Andrade, E. X. L., Bracciali, Cleonice Fátima, Sri Ranga, A.   +2 more
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A probabilistic model for quadrature rules

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Masjed-Jamei, Mehdi Dehghan 0002
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Quadrature rules for rational functions

Numerische Mathematik, 2000
Recent ideas on Gauss-type quadrature rules are extended to Gauss-Kronrod, Gauss-Turán and Cauchy principal value quadrature rules. Numerical examples supporting the theory are given.
GAUTSCHI W., GORI L., LO CASCIO, Maria Laura   +2 more
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On the computation of Patterson-type quadrature rules

Journal of Computational and Applied Mathematics, 2022
The Gauss-Kronrod formula is a \((2n+1)\)-point interpolating quadrature formula for \(I[f]=\int_{-1}^1 f(x)d\mu(x)\). It has \(n\) Gauss nodes (zeros of orthogonal polynomial \(p_n\)), and the remaining \(n+1\) nodes are zeros of a the Stieltjes polynomial \(Q_{n+1}\) (orthogonal to \(p_n(x) x^k\), \(k=0,\ldots,n\)) [\textit{D. Calvetti} et al., Math.
Bernardo de la Calle Ysern, Miodrag M. Spalevic   +1 more
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Quadrature Rules Based on the Arnoldi Process

SIAM Journal on Matrix Analysis and Applications, 2005
Applying a few steps of the Arnoldi process to a large nonsymmetric matrix \(A\) with initial vector \(v\) is shown to induce several quadrature rules. Properties of these rules are discussed, and their application to the computation of inexpensive estimates of the quadratic form \(\langle f,g\rangle:=v^\ast(f(A))^\ast g(A)v\) and related quadratic and
Daniela Calvetti, Sun-Mi Kim, Lothar Reichel   +2 more
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Quadrature rules for Prandtl's integral equation

Computing, 1986
We construct an interpolatory quadrature formula of the type \[ \int^{1}_{-1}f'(x)/(y-x)dx\approx \sum^{n}_{i=1}w_{ni}(y)f(x_{ni}), \] where \(f(x)=(1- x)^{\alpha}(1+x)^{\beta}f_ 0(x)\), \(\alpha,\beta >0\), and \(\{x_{ni}\}\) are the n zeros of the n-th degree Chebyshev polynomial of the first kind, \(T_ n(x)\).
MONEGATO, Giovanni, Pennacchietti V.
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The set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges’ sense

Journal of Computational and Applied Mathematics
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Nevena Z. Petrovic, Miroslav S. Pranic, Marija P. Stanic, Tatjana V. Tomovic Mladenovic   +3 more
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On Functional Equations Connected with Quadrature Rules

gmj, 2009
Abstract The functional equations of the form are considered. They are connected with quadrature rules of the approximate integration. We show that such equations characterize polynomials in the class of continuous functions.
Koclȩga-Kulpa, B., Szostok, T., Wasowicz, S.   +2 more
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Hybrid Gauss-Trapezoidal Quadrature Rules

SIAM Journal on Scientific Computing, 1999
The author derives a new class of quadrature rules prescribed for regular and for singular functions as well. The most important property is the fact that the quadrature weights of these rules are positive and the class includes rules of arbitrarily high-order convergence.
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