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An improved algorithm of grey model-GM(1,1) based on total least squares and its application in deformation forecast

机译:基于总最小二乘的灰色模型-GM(1,1)改进算法及其在变形预测中的应用

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This paper presents an improved algorithm for grey model-GM(1,1) based on total least squares (TLS). As we know that the parameters a and b in grey model-GM(1,1) can be solved by the least squares method. The LS method is based on an assumption that vector Y contains errors while repeated additive matrix B is accurate in GM(1,1). When we analyze the element of matrix B, the matrix B also contains errors in fact. TLS is the method of fitting that is appropriate when there are errors in both vector Y and matrix B. The calculated results of an example show that the prediction model based on TLS can enhance the prediction accuracy.
机译:本文提出了一种基于总最小二乘(TLS)的灰色模型GM(1,1)的改进算法。我们知道,灰色模型-GM(1,1)中的参数a和b可以通过最小二乘法求解。 LS方法基于以下假设:向量Y包含错误,而重复的加法矩阵B在GM(1,1)中是准确的。当我们分析矩阵B的元素时,矩阵B实际上也包含错误。 TLS是当向量Y和矩阵B都存在错误时的适合方法。实例计算结果表明,基于TLS的预测模型可以提高预测精度。

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