The complex variable interpolating moving least-squares method

In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented first. Considering the unclear physical meaning of the functional in the existing complex variable moving least-squares (CVMLS) approximation, an improved CVMLS approximation is presented by constructing a new functional with an explicit physical meaning. Based on the improved CVMLS approximation, the complex variable interpolating moving least-squares (CVIMLS) method is presented, and the interpolating property of the corresponding shape function of the CVIMLS method is proved.