On polynomial matrix spectral factorization by symmetric extraction
On polynomial matrix spectral factorization by symmetric extraction
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基于对称提取的多项式矩阵谱分解
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发表时间：
1985
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通讯作者：
F. Callier
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作者：
F. Callier
本文通过提取对称因子的方法，修正了1963年的Davis算法[2]，该算法不考虑无穷远处的零点，可用于仿Hermitian非负多项式矩阵Phi的谱分解.通过引入φ的对角约化的概念，我们得到了一个简单的充分测试的零点在无穷远。然后，我们展示了如何得到φ，对角减少对角过剩减少步骤（类似于大野和安浦步骤），删除所有零在无穷大，然后如何删除同步有限零，同时保持el，对角减少（因此，免费的零在无穷大）。这导致在一个修正的对称提取谱分解算法与单调度控制。一个例子显示了教学的概念简单的方法。通过修正和发现多项式矩阵的重要的单边因子提取性质，发现了适当的对称提取。
We revise the 1963 Davis algorithm [2] for the spectral factorization of a para-Hermitian nonnegative polynomial matrix Phi , by symmetric factor extraction: this algorithm is careless about zeros at infinity. By introducing the notion of diagonal reducedness of Phi , we obtain an easy sufficient test for the absence of zeros at infinity. We show then how to get Phi , diagonally reduced by diagonal excess reduction steps (similar to the Oono and Yasuura steps), removing all zeros at infinity, and then how to remove synunetrically finite zeros while keeping el, diagonally reduced (hence, free of zeros at infinity). This results in a revised symmetric extraction spectral factorization algorithm with monotone degree control. An example shows the didactical conceptual simplicity of the method. Appropriate symmetric extraction is discovered by revising and discovering important particular one-sided factor extraction properties of polynomial matrices.