A Characterization of Positive Quadrature Formulae

DOI10.2307/2153531zbMath0799.65020OpenAlexW2048973462MaRDI QIDQ4292057

Yuan Xu

Publication date: 1 June 1994

Full work available at URL: https://doi.org/10.2307/2153531

zbMATH Keywords

characteristic polynomialssymmetric tridiagonal matrixquasi-orthogonal polynomialspositive quadrature formulae

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Appell, Horn and Lauricella functions (33C65)

Related Items (20)

Numerical Integration in Multiple Dimensions with Designed Quadrature ⋮ On quasi-orthogonal polynomials: their differential equations, discriminants and electrostatics ⋮ Quadrature formulae and polynomial inequalities ⋮ On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials ⋮ Extended Lagrange interpolation and nonclassical Gauss quadrature formulae ⋮ Some properties of zeros of Sobolev-type orthogonal polynomials ⋮ Orthogonality of quasi-orthogonal polynomials ⋮ Polynomial interpolation on the unit sphere. II ⋮ Quasi-orthogonality and zeros of some \({}_2 \phi_2\) and \({}_3 \phi_2\) polynomials ⋮ Cubature formulae and orthogonal polynomials ⋮ Orthogonal polynomials associated with an inverse quadratic spectral transform ⋮ A new family of extended Gauss quadratures with an interior interval constraint ⋮ Positive quadrature formulas III: asymptotics of weights ⋮ Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials ⋮ Cubature rules for unitary Jacobi ensembles ⋮ Algebro-geometric aspectsof the Christoffel-Darboux kernelsfor classical orthogonal polynomials ⋮ On almost tight Euclidean designs for rotationally symmetric integrals ⋮ Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations ⋮ A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations ⋮ Weighted nonstandard quadrature formulas based on values of linear differential operators

Cites Work

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• A note on positive quadrature rules
• Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices
• Quasi-orthogonal polynomials, quadrature, and interpolation
• Numerical integration rules near Gaussian quadrature
• A class of orthogonal polynomials
• Characterization of Quadrature Formula II
• Characterization of Positive Quadrature Formulas
• Weight Functions for Chebyshev Quadrature

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