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|Paper IPM / M / 14972||
In this paper a direct approximation method on the sphere, constructed by generalized moving least squares, is presented and analyzed. It is motivated by numerical solution of partial differential equations on spheres and other manifolds. The new method generalizes the finite difference methods, someway, for scattered data points on each local subdomain. As an application, the Laplaceï¿½??Beltrami equation is solved and the theoretical and experimental results are given. The new approach eliminates some drawbacks of the previous methods.
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