【摘要】 建模方法是时间序列分析的核心问题之一。本文给出了两种基于最小二乘法的自回归模型(AR模型)的建模方法。采取预留少量数据递补进入计算的办法,使矩阵XTX可以用分块矩阵求逆公式递推求逆,或者用矩阵的Crout分解法递推求解。同时引入了Winograd向量内积快速算法,充分利用各向量和各矩阵之间的关系来减少计算工作量。使计算量比一般最小二乘建模方法大幅度减少,达到与Marple算法和Burg的最大熵谱法可比的程度。更多还原

【Abstract】 Method of modelling is a major question of the time series analysis. Two modelling methods of autoregressive ( AR ) model based on the LS approach are proposed in this paper.By means of reserving a few data to enter calculating successively,the matrix XTX can be inversed recursively by the inver-sing formula of block matrix or result from the Crout resolving method. Moreover, a quick scalar product algorithm, advanced by S. Winograd, is emp- loyed and the relations between vectors or matrices are applied for reducing computational operations.The operations have been largely reduced so that they are less than the operations of normal LS approach, and they can be compared with the famous Marple algorithm and Burg’s maximum entropy spectral analysis method.更多还原