Abstract

Because of its extensive appearance and application in scientific research and industrial production, the matrix square root problem has received massive attention and study. In this paper, based on our previous work, by using zeroing neural dynamics (ZND) method, a continuous-time dynamic matrix square root (CTDMSR) model is given at first. Besides, a general ten-instant Zhang et al. discretization (ZeaD) formula is derived, constructed and investigated, and the corresponding theoretical analysis is provided. Next, by applying this general formula to discretize the CTDMSR model, a general ten-instant discrete-time dynamic matrix square root (DTDMSR) model with sixth-order precision is further obtained. For comparison purposes, four DTDMSR models, with the second-, third-, fourth-, and fifth-order precision, are also acquired and presented, respectively, by using other ZeaD formulas. At last, the effectiveness and correctness of the proposed DTDMSR models for dynamic matrix square root finding are further substantiated by numerical experimental results.

摘要

矩阵平方根问题由于其广泛的出现和在科研和工业生产中的应用而受到了广泛的关注和研究。本文在前人工作的基础上，通过归零神经动力学（ZND）方法，首先给出了连续时间动态矩阵平方根（CTDMSR）模型。此外，还有十个普通的张等人。推导，构造和研究了离散化（ZeaD）公式，并提供了相应的理论分析。接下来，通过应用该通用公式离散化CTDMSR模型，可以进一步获得具有六阶精度的通用十瞬时离散时间动态矩阵平方根（DTDMSR）模型。为了进行比较，还获取并展示了具有二阶，三阶，四阶和五阶精度的四个DTDMSR模型，分别使用其他ZeaD公式。最后，数值实验结果进一步证实了所提出的DTDMSR模型用于动态矩阵平方根查找的有效性和正确性。