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...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.展开更多
基金Project supported by the Key Program of the National Natural Science Foundation of China(No.11131006)the National Natural Science Foundation of China(Nos.61075054,90818020,60873206)
文摘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.
