A look-ahead Levinson algorithm for general Toeplitz systems
A look-ahead Levinson algorithm for general Toeplitz systems
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DOI：
10.1109/78.134471
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发表时间：
1992-05
期刊：
影响因子：
--
通讯作者：
T. Chan;P. Hansen
中科院分区：
文献类型：
--
作者：
T. Chan;P. Hansen
作者提出了一个扩展的Levinson的算法，保证是弱稳定的一大类一般Toeplitz矩阵，即那些没有许多连续的病态领导主子矩阵。新算法通过跳过求解过程中遇到的所有病态的主要子矩阵来适应给定的Toeplitz矩阵。这是通过一个前瞻性的战略，监测领先的主子矩阵的条件，如果必要的话，切换到一个合适的大小块步骤。与经典的Levinson算法相比，前瞻算法的开销通常很小，并且还产生了可靠的条件数估计。>
The authors present an extension of Levinson's algorithm that is guaranteed to be weakly stable for a large class of general Toeplitz matrices, namely, those that do not have many consecutive ill-conditioned leading principal submatrices. The new algorithm adapts itself to the given Toeplitz matrix by skipping over all the ill-conditioned leading principal submatrices encountered during the solution process. This is done by a look-ahead strategy that monitors the condition of the leading principal submatrices and, if necessary, switches to a block step of suitable size. The overhead of the look-ahead algorithm is typically small compared to the classical Levinson algorithm, and in addition a reliable condition number estimate is produced. >