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AR模型的兩種計算量較小的建模方法

Two Modelling Methods of AR with Less Computational Operations

  • 摘要: 建模方法是時間序列分析的核心問題之一。本文給出了兩種基于最小二乘法的自回歸模型(AR模型)的建模方法。采取預留少量數據遞補進入計算的辦法,使矩陣XTX可以用分塊矩陣求逆公式遞推求逆,或者用矩陣的Crout分解法遞推求解。同時引入了Winograd向量內積快速算法,充分利用各向量和各矩陣之間的關系來減少計算工作量。使計算量比一般最小二乘建模方法大幅度減少,達到與Marple算法和Burg的最大熵譜法可比的程度。

     

    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 employed 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.

     

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