A Recursive Householder Transformation Formula and its Applications
矩阵上三角化的递推Householder变换公式及其应用

A recursive Householder formula for transforming high rectangular matrices into upper triangular matrices column by column is proposed. The formula can be used to simultaneously estimate the orders and parameters of polynomial models, difference models, AR models, ARMA models, CARMA models and so on. Since the orders can be estimated in passing by our formula, the computation time for estimating both orders and parameters is only slightly more than that for just estimating the parameters of the model with known orders.