论文标题
基于自适应过滤技术的矩阵符号功能的两种迭代算法
Two Iterative algorithms for the matrix sign function based on the adaptive filtering technology
论文作者
论文摘要
在本文中，通过将过滤算法与牛顿方法和牛顿·舒尔茨方法相结合，提出了两种用于计算大规模稀疏基质符号函数的新有效算法。通过对迭代过程中误差扩散的理论分析，我们设计了一个自适应过滤阈值，这可以确保过滤对迭代过程和计算结果的影响很小。数值实验与我们的理论分析一致，这表明我们方法的计算效率比牛顿方法和牛顿·舒尔茨方法的计算效率要好得多，并且计算误差与两种方法的数量级相同。
In this paper, two new efficient algorithms for calculating the sign function of the large-scale sparse matrix are proposed by combining filtering algorithm with Newton method and Newton Schultz method respectively. Through the theoretical analysis of the error diffusion in the iterative process, we designed an adaptive filtering threshold, which can ensure that the filtering has little impact on the iterative process and the calculation result. Numerical experiments are consistent with our theoretical analysis, which shows that the computational efficiency of our method is much better than that of Newton method and Newton Schultz method, and the computational error is of the same order of magnitude as that of the two methods.
