The structured condition number of the solution of the Yule-Walker system of equations is given. It is found that there is little difference between this structured condition and the general condition number of a Toeplitz matrix. As a consequence, general purpose linear system solvers are stable for solving the Yule-Walker equations. By constructing appropriate examples it is shown that the Levinson algorithm is only weakly stable and is less trustworthy than the LDL$+T$/ algorithm. Our round-off error analysis also suggests that for better accuracy Schur coefficients should be computed by the Schur algorithm and then used in the Levinson algorithm for computing the solution of Yule-Walker equations.
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机译：给出了等式的yule-walker系统的结构的结构化状态。发现这种结构化条件与Toeplitz矩阵的一般条件数之间几乎没有差异。因此，通用线性系统溶剂是稳定求解Yule-Walker方程的稳定性。通过构建适当的示例，示出了Levinson算法仅弱稳定，并且不如LDL $ + T $ /算法的信任。我们的圆截止错误分析还表明，对于更好的精度SCHUR系数，应由SCCUR算法计算，然后在Levinson算法中使用以计算Yule-Walker方程的解决方案。
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