By Arieh Iserles
Acta Numerica surveys each year an important advancements in numerical research. the themes and authors, selected via a special foreign panel, supply a survey of articles notable of their caliber and breadth. This quantity contains articles on multivariate integration; numerical research of semiconductor units; quickly transforms in utilized arithmetic; complexity concerns in numerical research.
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Additional info for Acta Numerica 1997 (Volume 6)
Let me whet your appetite. A cubature formula is meant to be used to approximate integrals. Users want to have an indication of the accuracy of the approximation. A classical way to obtain an error estimate is to compare several approximations of different degrees of precision. Sequences of embedded cubature formulae help to reduce the burden. Indeed, these have already been investigated. As Cools (1992) incorporates a survey of some of the obtained results, I resist the temptation to elaborate on this subject.
30, 1-23. J. N. Lyness (1992), On handling singularities in finite elements, in Numerical Integration - Recent Developments, Software and Applications (T. Espelid and A. Genz, eds), Vol. 357 of NATO ASI Series C: Math, and Phys. Sciences, Kluwer, Dordrecht, pp. 219-233. J. N. Lyness and R. Cools (1994), A survey of numerical cubature over triangles, in Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (W. ), Vol. 48 of Proceedings of Symposia in Applied Mathematics, AMS, Providence, RI, pp.
Both conditions lead to necessary conditions for 7^: linear and quadratic equations in the ~fijS. 1. The 5-method has been used to construct cubature formulae of degree 13 with 36, 35 and 34 points for C2, 52, £7 > a n d of degree 17 with 57 points for C 2 . 4- Evaluation Orthogonal polynomials and ideal theory are powerful tools for theoretical investigations of cubature formulae. The most complex concepts of ideal theory have only been used to develop construction methods and to prove theorems about cubature formulae.
Acta Numerica 1997 (Volume 6) by Arieh Iserles