Quasi-interpolation Operators On Parallel Dodecahedrom With High Approximation Orders In Spaces Of Polyharmonic Splines

The Qusai-interpolation is an important approach of function approximating.Comparing with Interpolation and Least Squares,the Qusai-interpolation doesn’t need to solve the linear system,and has a better application in CAGD,PDE and Computational Geometry,etc.In this paper,we base on the approach which Milvia Rossini released in[1]（the approach is using the m harmonic spline to approximate data given on hexagonal lattices in 2 dimension）,we construct the Qusai-interpolation on the parallel dodecahedron in 3 dimension.Then by a procedure which starts from a generatorΦ₀^Γ,we obtain theΦ₀^Γ,Φ₁^Γ,...,Φ_m-1^Γwhich Qusai-interpolation operators reproducing polynomials up to a higher degree and faster in decay,which the reproducing polynomials are belongs top₁,p₃,...,p_2m-1Finally,we show some numerical experiments,compute and compare the error of Φ₀^Γ,Φ₁^Γ,Φ₂^Γ.The results show that the operator we construct has a good validity.