## Numerical integration: recent developments, software, and applicationsThis volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks. The papers are organized into four parts: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software; many papers are relevant to more than one category. The workshop studied the state of the art in numerical integration (both single and multidimensional). The book contains a number of survey papers by experts on themes such as: numerical solution of integral equations, cubature formulae construction, handling singularities in finite elements, statistical applications, lattice rules, error estimates, error bounds and software. |

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### Contents

Karin Gatermann | 25 |

KlausJiirgen Forster | 45 |

Harald Niederreiter | 71 |

Copyright | |

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### Common terms and phrases

1992 Kluwer Academic adaptive integration affine transform analytic applied asymptotic automatic integration basic rule Bergen Berntsen boundary element boundary element method Cauchy principal value Comp Computer Science construction convergence cubature formulae cubature rule DCUHRE DCUTRI defined denote dimensional error bounds error estimating procedure error expansion error functional example Figure finite formula of degree Gaussian Quadrature Gaussian rules Gem eds Genz given Hammerlin hypercube hyperrectangles IMT-transformation integral equations integrand integrand function invariant iterated lattice rules Lemma Levin transformation linear Lyness Macsyma Math method nodes null rules number of function Numerical Integration obtained orthogonal polynomials parameters Peano kernels polynomials of degree problem quadrature error quadrature formula quadrature rule Rabinowitz region processor rules of degree sequence Sloan spline subdivision subroutine symmetric T. O. Espelid Theorem theory triangle TRIEX TRILEV truncated power functions u-transformation variable vector weight function zero