Estimation and application of matrix eigenvalues based on deep neural network

In today's era of rapid development in science and technology, the development of digital technology has increasingly higher requirements for data processing functions. The matrix signal com-monly used in engineering applications also puts forward higher requirements for processing speed. The eigenvalues of the matrix represent many characteristics of the matrix. Its mathematical meaning repre-sents the expansion of the inherent vector, and its physical meaning represents the spectrum of vibration. The eigenvalue of a matrix is the focus of matrix theory. The problem of matrix eigenvalues is widely used in many research fields such as physics, chemistry, and biology. A neural network is a neuron model con-structed by imitating biological neural networks. Since it was proposed, the application research of its typical models, such as recurrent neural networks and cellular neural networks, has become a new hot spot. With the emergence of deep neural network theory, scholars continue to combine deep neural net-works to calculate matrix eigenvalues. This article aims to study the estimation and application of matrix eigenvalues based on deep neural networks. This article introduces the related methods of matrix eigen-value estimation based on deep neural networks, and also designs experiments to compare the time of matrix eigenvalue estimation methods based on deep neural networks and traditional algorithms. It was found that under the serial algorithm, the algorithm based on the deep neural network reduced the calculation time by about 7% compared with the traditional algorithm, and under the parallel algorithm, the calculation time was reduced by about 17%. Experiments are also designed to calculate matrix eigen-values with Obj and recurrent neural networks (RNNS) models, which proves that the Oja algorithm is only suitable for calculating the maximum eigenvalues of non-negative matrices, while RNNS is commonly used in general models.