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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >The Field of Values of a Matrix and Neural Networks
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The Field of Values of a Matrix and Neural Networks

机译：矩阵和神经网络的价值领域

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摘要

The field of values of a matrix, also known as the numerical range, is introduced in the context of neural networks. Using neural network techniques, an algorithm and a generalization are developed that find eigenpairs of a normal matrix. The dynamics of the algorithm can be observed on the complex plane. Only limited visualization is possible in the case when the matrix is Hermitian (or real symmetric) since the field of values is confined on the real line. The eigenpairs can serve as stored memories, which are recalled by using the algorithm. Shifting in the algorithm is also discussed, which assists in finding other eigenpairs. Trajectories of runs of the algorithm are visually presented, through which the behavior of the algorithms is elucidated.
机译：在神经网络的背景下介绍了矩阵值的字段，也称为数值范围。使用神经网络技术，开发了一种算法和归纳法，可以找到正常矩阵的本征对。可以在复杂平面上观察算法的动力学。在矩阵为Hermitian（或实对称）的情况下，只有有限的可视化是可能的，因为值的字段限制在实线上。本征对可以用作存储的内存，可以通过使用算法来调用。还讨论了算法的移位，该移位有助于查找其他特征对。直观地显示了算法的运行轨迹，从而阐明了算法的行为。

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