Existence of solutions to systems of underdetermined equations and spherical designs

被引:41
作者
Chen, Xiaojun [1 ]
Womersley, Robert S.
机构
[1] Hirosaki Univ, Dept Math Sci, Hirosaki, Aomori 0368561, Japan
[2] Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia
关键词
verification; underdetermined system; spherical designs; extremal points; interpolation; numerical integration;
D O I
10.1137/050626636
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is concerned with proving the existence of solutions to an underdetermined system of equations and with the application to existence of spherical t-designs with (t + 1)(2) points on the unit sphere S-2 in R-3. We show that the construction of spherical designs is equivalent to solution of underdetermined equations. A new veri. cation method for underdetermined equations is derived using Brouwer's fixed point theorem. Application of the method provides spherical t-designs which are close to extremal (maximum determinant) points and have the optimal order O(t(2)) for the number of points. An error bound for the computed spherical designs is provided.
引用
收藏
页码:2326 / 2341
页数:16
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