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Numerical Algorithms

, Volume 79, Issue 2, pp 423–435 | Cite as

Convergent interpolatory quadrature rules and orthogonal polynomials of varying measures

  • Ulises Fidalgo
  • Erwin Miña-Díaz
Original Paper

Abstract

Let (P n ) be a sequence of polynomials such that P n (x) > 0 for x ∈ [− 1, 1] and \(\lim \limits _{n\to \infty }\text {deg}(P_{n})/n = 1\). Let q n be the nth monic orthogonal polynomial with respect to \( {P}_{n}^{-1} \) d μ, where μ is a measure on [− 1, 1] that is regular in the sense of Stahl and Totik. We prove that the interpolatory quadrature rule with nodes at the zeros of q n is convergent with respect to μ provided that the zeros of P n lie outside a certain curve surrounding [− 1, 1].

Keywords

Interpolatory quadrature formulas Orthogonal polynomials Varying measures 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Case Western Reserve UniversityClevelandUSA
  2. 2.The University of MississippiUniversityUSA

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