Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 22, Issue 3, pp 339-352

First online:

The number of positive weights of a quadrature formula

  • G. SottasAffiliated withSection de mathématiques, Université de Genève
  • , G. WannerAffiliated withSection de mathématiques, Université de Genève

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Abstract

In this paper we show that the number of positive weights of a quadrature formula is related to the number of rotations of a certain path in the plane. Necessary and sufficient conditions for all weights to be positive can then be obtained. Also, much of classical theory appears in a new light.