【摘要】 参考文献[1]介绍了通过简单变换x=z-z0/h将步长为h的等距节点z0,z1…,zn转换成x=0,1,2,…,n的整数点,然后利用已知的整数节点的正交多项式系对其进行拟合;而对于散乱节点,参考文献[2]利用施密特正交化的方法获得其正交多项式系,然后进行正交多项式拟合．只是施密特正交化方法的运算量比较大,能否类似于等距节点利用简单的数学变换实现散乱节点的正交多项式拟合,也是一个值得考虑的问题．本文利用插值变换将散乱节点转换成整数点,从而实现散乱节点的正交多项式拟合．更多还原

【Abstract】 In literature [1] , it is introduced that changing the equally spaced points z0,z1 ,…,zn with step h into x = 0 ,1,…, n through the simple transform x = z-z0/h, and we can fit them making use of orthogonal polynomials of integer nodes. For the random nodes, it is introduced that we can orthogonalize them through the method of Schmidt orthogonalization in literature [2]. Then we can fit them making use of orthogonal polynomials. But the method of Schmidt orthogonalization, its computing quantity is greater. Hence it is worthy to be considered whether we can realize the fitting of an orthogonal polynomial of arbitrary random nodes through the simple transaction similarly as equally spaced points. In this paper, we have realized the fitting of an orthogonal polynomial of arbitrary random nodes through the interpolating transaction which changes the arbitrary random nodes into integer nodes.更多还原