Inertia properties of indefinite quadratic forms
Inertia properties of indefinite quadratic forms
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DOI：
10.1109/97.484217
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发表时间：
1996-02
影响因子：
3.9
通讯作者：
A. H. Sayed;B. Hassibi;T. Kailath
中科院分区：
文献类型：
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作者：
A. H. Sayed;B. Hassibi;T. Kailath
研究了两个不定二次型估计问题的解之间的关系。我们表明，这两种解决方案之间的完整联系，可以通过调用一组基本的惯性条件。虽然这些惯性条件在标准希尔伯特空间中自动满足，但它们却标志着不确定度量空间中两个估计问题之间的差异。它们还包括，作为特殊情况下，众所周知的H/sup -/spl infin//-过滤器和控制器的存在条件。给定两个厄米特矩阵{/spl Pi/，W}，一个列向量y和一个适当维数的任意矩阵A，研究了两个二次代价函数极小化问题之间的关系，同时也涉及到不定权最小二乘问题.
We study the relation between the solutions of two estimation problems with indefinite quadratic forms. We show that a complete link between both solutions can be established by invoking a fundamental set of inertia conditions. While these inertia conditions are automatically satisfied in a standard Hilbert space setting, they nevertheless turn out to mark the differences between the two estimation problems in indefinite metric spaces. They also include, as special cases, the well-known conditions for the existence of H/sup -/spl infin//-filters and controllers. Given two Hermitian matrices {/spl Pi/, W}, a column vector y, and an arbitrary matrix A of appropriate dimensions, we study the relation between two minimization problems with quadratic cost functions, and also refer to the indefinite-weighted least-squares problem.