基于外推样条下伴有压缩因子的分形函数的推广缺项插值问题的研究

GENERALIZED FRACTAL LACUNARY INTERPOLATION WITH VARIABLE SCALING PARAMETERS BASED ON EXTRAPOLATION SPLINE

本文研究了分形函数的一般(0,m)缺项插值问题.利用外推样条函数作为插值基函数的方法,得到了当压缩因子满足‖αk(r)‖∞≤1/((2N)m)(k=1,2,…,N;r=0,1,…,m)时的(0,m)分形缺项插值函数,并得到了对应条件下的收敛结果,用数值算例验证了外推样条函数作为分形缺项插值基函数是可行和有效的。

In this paper,the generalized Birkhoff(0,m)lacunary interpolation problem for the fractal function with proper perturbable parameters is investigated.An extrapolation algorithm is proposed to obtain an approximate spline polynomial solution,and convergence estimates are presented under the assumption of‖αk(r)‖∞≤1/((2 N)m)(k=1.2,…,N;r=0,1,…,m).The numerical results show that the interpolate perturbation method we provide works effectively.