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In this study, we proposed a novel complex neural network model, which extends the neural networks based approaches that can asymptotically compute the largest imaginary part or the largest real part of eigenvalues to the case of directly calculating the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvectors of a real matrix. The proposed neural network algorithm is described by a group of complex differential equations. And the algorithm has parallel processing ability in an asynchronous manner and could achieve high computing capability. This paper also provides a rigorous mathematical proof for its convergence for a more clear understanding of network dynamic behaviors relating to the computation of the eigenvector and the eigenvalue. Numerical examples showed that the proposed algorithm has good performance for a general real matrix. Keywordscomplex neural network; real matrix; maximum sum of real part and imaginary part; eigenvalue; eigenvector

A Novel Neural Network Model for Extracting the Largest Sum of Real Part and Imaginary Part of Eigenvalues and the Corresponding Eigenvectors of a Real Matrix