On the pseudoinverse of a sum of symmetric matrices with applications to estimation
On the pseudoinverse of a sum of symmetric matrices with applications to estimation
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关于对称矩阵之和的伪逆及其在估计中的应用
DOI：
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发表时间：
1979
期刊：
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通讯作者：
P. Kovanic
中科院分区：
文献类型：
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作者：
P. Kovanic
给出了一个新的对称矩阵和的伪逆的计算公式，该公式适用于任意对称矩阵，不受行、列空间的限制。作为该公式的一个应用，发展了最小化惩罚的广义估计。这使得有可能表明，在一般情况下的估计问题被分解成两个独立的问题。其中之一是有关的数据属于一个子空间包含信号分量，但没有噪声分量。这部分问题可以很容易地解决，对这部分数据进行估计的结果是无误差的。
A new formula for the pseudoinverse of a sum of symmetric matrices is presented, valid for arbitrary symmetric matrices without any restrictions relating to their column — or row — spaces. As an application of this formula a generalized version of the estimate minimizing the penalty is developed. This makes it possible to show that in a general case of estimation the problem is decomposed into two independent problems. One of them is related to data belonging to a subspace containing signal components but no noise components. This part of the problem can be easily solved, the result of estimation performed on this part of data being error-free.