Zhang Neurodynamics for Cholesky Decomposition of Matrix Stream Using Pseudo-Inverse with Transpose of Unknown

Cholesky decomposition is a well-known decomposition for positive definite matrix. On account of its significantly fundamental roles in linear algebra and matrix theory, there are a lot of researches and applications based on it. In recent years, solving time-varying problems has been a research hotspot, but Cholesky decomposition of matrix stream (i.e., continuous time-varying matrix) in a simple, direct and effective equation-solving manner remains a challenging issue. In this paper, the problem of Cholesky decomposition of matrix stream is attempted and solved. First, with the aid of Zhang neurodynamics (ZN), the objective equation at time-derivative level, including the time derivatives of matrix variable and its transpose, is obtained. In order to handle the objective equation with transpose of unknown, Kronecker product, vectorization technique and vectorized transpose matrix are utilized for better derivation. Thus, a ZN solution model using pseudo-inverse is proposed and numerically experimented. Finally, numerical experiment results substantiate the efficacy of the pseudo-inverse type ZN solution model.