Can a minimal degree 6 cubature rule for the disk have all points inside?
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摘要
We use positivity and extension properties of moment matrices to prove that a 10-node (minimal) cubature rule of degree 6 for planar measure on the closed unit disk D¯ cannot have all nodes in D¯. We construct examples showing that such rules may have as many as 9 points in D¯, and we provide similar examples for the triangle.
论文关键词：Primary: 47A57,Secondary: 44A60,65D32,Cubature rules,Positive moment matrix,Flat extensions
论文评审过程：Received 20 February 2004, Revised 31 January 2005, Available online 16 March 2005.
论文官网地址：https://doi.org/10.1016/j.cam.2005.02.001
