灰色系统模型病态矩阵的双正则化算法

A Double Regularization Method for Ill-Conditioned Matrix in Gray System Model

灰色系统模型矩阵会存在病态问题.为消除其病态性,基于病态矩阵的双正则化方法,建立了正则化灰色系统模型中灰参数求解的表达式,给出了其导出方式;提出了正则参数α的选择原则.从而避免了灰参数求解过程中矩阵的病态问题.数值试验分析说明,灰色系统模型的双正则化算法是正确和适用的.

Matrix in general grew system model exists ill-posed problem.To eliminate illposed phenomena,based on the irregular method of pathological matrix method,formula for solving grey parameter of regularization algorithm of the grey system model is established.Derived method is also given.Selection principle of regularization parameter is proposed so the ill-conditioned matrix problem was avoided in solving grey parameter process.Numerical experiment and analysis showed that the regularization algorithm of grey system model is accuracy and applicability.