This work is a natural extension of the work done in Part II of this series. A new partition of unity | the synchronized reproducing kernel (SRK) interpolant|is proposed within the framework of moving least square reproducing kernel representation. It is a further development and generalization of the reproducing kernel particle method (RKPM), which demonstrates some superior computational capa...

In Part I of this work, the moving least-square reproducing kernel (MLSRK) method is formulated and implemented. Based on its generic construction, an m-consistency structure is discovered and the convergence theorems are established. In this par\ of the work, a systematic Fourier analysis is employed to evaluate and further establish the method. The preliminary Fourier analysis reveals that th...