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 ...
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ISBN:
(纸本)9789881563804
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.
Time-dependent Cholesky factorization is investigated and solved further in this *** improved solution model via Zhang neuronet(ZN) is proposed with constraint conditions *** first,we combine the objective equations a...
详细信息
ISBN:
(数字)9789887581536
ISBN:
(纸本)9781665482561
Time-dependent Cholesky factorization is investigated and solved further in this *** improved solution model via Zhang neuronet(ZN) is proposed with constraint conditions *** first,we combine the objective equations and constraint conditions into new *** final coefficient matrix of the new equations(as an equation group) is ***,the new equations are solved by using *** improved ZN solution model accurately solves the problem,and it exponentially converges to the theoretical *** experiments and results substantiate the efficacy and the superiority of the improved ZN solution model.
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 ...
详细信息
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 timevarying 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.
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