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“School of Mathematics”

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Paper   IPM / M / 14972
School of Mathematics
  Title:   Direct approximation on spheres using generalized moving least squares
  Author(s):  D. Mirzaei
  Status:   Published
  Journal: BIT Numer. Math.
  Year:  2017
  Pages:   DOI: 10.1007/s10543-017-0659-8
  Supported by:  IPM
  Abstract:
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 Laplace�??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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