Linear Combinations of Orthogonal Polynomials Generating Positive Quadrature Formulas

DOI10.2307/2008802zbMath0708.65022OpenAlexW4251640205MaRDI QIDQ3490844

Franz Peherstorfer

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2008802

zbMATH Keywords

orthogonal polynomialsGaussian rulespositive weightsnumerical interpolatory quadrature formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (22)

Some properties of zeros of Sobolev-type orthogonal polynomials ⋮ Orthogonality of quasi-orthogonal polynomials ⋮ Zeros of linear combinations of orthogonal polynomials ⋮ Positivity of the Weights of Extended Clenshaw-Curtis Quadrature Rules ⋮ Weight functions admitting repeated positive Kronrod quadrature ⋮ Zeros of orthogonal polynomials generated by canonical perturbations of measures ⋮ Szegö polynomials: Quadrature rules on the unit circle and on \([-1,1\)] ⋮ Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials ⋮ Positive trigonometric quadrature formulas and quadrature on the unit circle ⋮ Mixed recurrence relations and interlacing of the zeros of some \(q\)-orthogonal polynomials from different sequences ⋮ Generalized associated polynomials and functions of second kind ⋮ Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa ⋮ Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences ⋮ Positive quadrature formulas III: asymptotics of weights ⋮ Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials ⋮ A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: bounds, asymptotics and zeros ⋮ Interlacing of zeros of orthogonal polynomials under modification of the measure ⋮ Interlacing of the zeros of Jacobi polynomials with different parameters ⋮ Orthogonality properties of linear combinations of orthogonal polynomials ⋮ Zeros of linear combinations of Laguerre polynomials from different sequences ⋮ Interlacing and spacing properties of zeros of polynomials, in particular of orthogonal and \(L_q\)-minimal polynomials, \(q\in [1,\infty \)] ⋮ The zeros of linear combinations of orthogonal polynomials

Cites Work

• A note on positive quadrature rules
• Some positive Cotes numbers for the Chebyshev weight function
• The number of positive weights of a quadrature formula
• Numerical integration rules near Gaussian quadrature
• Characterization of Quadrature Formula II
• Characterization of Positive Quadrature Formulas
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