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

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.