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| Cubature Formula for Spherical Basis Function Networks |
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Citation： |
Shaobo LIN,Feilong CAO,Zongben XU,Xiaofei GUO.Cubature Formula for Spherical Basis Function Networks[J].Chinese Annals of Mathematics B,2012,33(6):807~814 |
| Page view： 1757
Net amount： 1449 |
Authors： |
Shaobo LIN; Feilong CAO; Zongben XU; Xiaofei GUO; |
Foundation： |
the Key Program of the National Natural Science Foundation of China (No.11131006) and the National Natural Science Foundation of China (Nos. 61075054, 90818020, 60873206). |
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| Abstract： |
Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere. Thus cubature formula plays an important role in computing these spherical integrals. This paper is devoted to establishing an exact positive cubature formula for spherical basis function networks. The authors give an existence proof of the exact positive cubature formula for spherical basis function networks,and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data. |
Keywords： |
Cubature formula, Spherical basis function, Scattered data |
Classification： |
41A25, 41A05, 41A63 |
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