论文标题
一个新的稳定和避免反转迭代，用于计算矩阵平方根
A new stable and avoiding inversion iteration for computing matrix square root
论文作者
论文摘要
这项研究的目的是计算具有稀疏近似值的主基质平方根。提供了一种新的稳定迭代方案，避免了完全基质反转（SIAI）。对迭代过程中涉及的矩阵的稀疏性和误差的分析进行了分析。根据带宽和误差分析，提出了将SIAI与滤波技术结合的更有效的算法。通过计算不同矩阵的主要平方根以揭示其在现有方法上的适用性来证明所提出方法的高计算效率和准确性。
The objective of this research was to compute the principal matrix square root with sparse approximation. A new stable iterative scheme avoiding fully matrix inversion (SIAI) is provided. The analysis on the sparsity and error of the matrices involved during the iterative process is given. Based on the bandwidth and error analysis, a more efficient algorithm combining the SIAI with the filtering technique is proposed. The high computational efficiency and accuracy of the proposed method are demonstrated by computing the principal square roots of different matrices to reveal its applicability over the existing methods.
