新型图形拟合方法的误差估计及应用

Error estimation and application of a new class of graphics fitting method

为了分析PIA方法的拟合误差和数学模型的收敛性以及收敛速度,给出PIA方法的拟合误计上界差估计公式.借助于PIA方法的配置矩阵迭代表示公式,以及经典的矩阵QR分解方法和矩阵L2-范数,给出PIA方法迭代次数预估公式.研究表明,PIA方法的拟合误差和拟合基函数、初始数据的参数化、配置矩阵的谱半径密切相关以及数值计算的舍入误差密切相关.在给定不同的拟合精度,以及不同的初始数据参数化的条件下,利用拟合误差估计公式,可以预估迭代拟合次数,提高拟合效果.

In order to analyze the fitting error and convergence of the mathematical model and the convergence rate of the progressive iterative approximation method （PIA）, we gave the formula of the bound of the fitting. By using the L2- matrix norm, the iterative collocation matrix formula of the PIA method and the classic QR matrix diagonalization method, we gave the formula for estimating the number of the iteration required by the PIA method in advance. Research showed that the fitting error of the PIA method is closely related to the rounding error of the calculation and the spectral radius of the collocation matrix and the initial parameterization of the given data points. Under the condition of the given different fitting precision and different initial parameterization of the given data points, using the estimation formula of the fitting error, the iterative number can be calculated and the fitting effect can be improved.