The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere

Document Type : Original Article


Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University


We present a new and simple direct approach based on generalized moving least squares (GMLS) for computing the first derivatives of the functions defined on the sphere. The novel method utilizes a Householder transformation (reflection) and a projection onto the tangent plane to compute the first derivatives at the original point on the sphere. The main benefit of this algorithm is that there is no need to use the spherical harmonics for constructing the approximation of the first derivatives. An example of the approximation has been tested to show the ability of the developed method. Moreover, this method has been applied to solve the transport equation in one example.

Graphical Abstract

The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere


Main Subjects

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Volume 8, Issue 1
In memory of Prof. Ali Reza Ashrafi
June 2023
Pages 35-42
  • Receive Date: 01 February 2023
  • Revise Date: 08 February 2023
  • Accept Date: 25 February 2023
  • Publish Date: 01 March 2023