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Gaussian quadrature formulas and Laguerre-Perron's equation

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Abstract

LetI(f) be the integral defined by:I(f) = ∫ a b f(x)w(x)dx withf a given function,w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value ofI(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

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Correspondence to S. El Hajji.

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Hajji, S.E., Touijrat, L. Gaussian quadrature formulas and Laguerre-Perron's equation. JAMC 18, 205–228 (2005). https://doi.org/10.1007/BF02936566

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AMS Mathematics Subject Classification

  • 33A65

Key words and phrases

  • Semi-classical orthogonal polynomials
  • Jacobi matrix
  • Laguerre-Perron's equation
  • nonclassical weight function
  • stability of the algorithm