CADRE

CADRE: An algorithm for numerical quadrature. This chapter discusses the program CADRE — an algorithm for numerical quadrature. The program employs an adaptive scheme whereby CADRE is found as the sum of estimates for the integral of F(x) over suitably small subintervals of a given interval of integration. Starting with the interval of integration itself as the first such subinterval, the program attempts to find an acceptable estimate on a given subinterval by cautious Romberg extrapolation. If this attempt fails, the subinterval is divided into two subintervals of equal length. For the sake of economy, values of F(x), once calculated, are saved until they are successfully used in estimating the integral over some subinterval to which they belong. The program CADRE uses the composite trapezoid sum. For certain classes of integrands, the composite trapezoid sum exhibits a known and characteristic convergence behavior that the algorithm attempts to detect and to exploit through cautious extrapolation.


References in zbMATH (referenced in 25 articles )

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  1. Gonnet, Pedro: Increasing the reliability of adaptive quadrature using explicit interpolants (2010)
  2. Chen, Chin-Yun: Bivariate product cubature using peano kernels for local error estimates (2008)
  3. Plaskota, Leszek; Wasilkowski, Grzegorz W.; Zhao, Yaxi: The power of adaption for approximating functions with singularities (2008)
  4. Shampine, L. F.: Vectorized adaptive quadrature in MATLAB (2008)
  5. Chen, Chin-Yun: Computing interval enclosures for definite integrals by application of triple adaptive strategies (2006)
  6. Plaskota, Leszek; Wasilkowski, Grzegorz W.: Adaption allows efficient integration of functions with unknown singularities (2005)
  7. Bialecki, B.; Keast, P.: A sinc quadrature subroutine for Cauchy principal value integrals (1999)
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  15. Miura, Robert M.: Accurate computation of the stable solitary wave for the FitzHugh-Nagumo equations (1982)
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