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.
Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signals
Istituto Nazionale di Alta Matematica（意大利高等数学研究所）；DISIM, Università degli Studi dell’Aquila（阿奎拉大学DISIM学院）；Gran Sasso Science Institute（格兰萨索科学研究所）；Libera Università di Bolzano（博尔扎诺自由大学）
Graph Iterative Filtering methods for the analysis of nonstationary signals on graphs
Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria（因苏布里亚大学科学与技术系）；Department of Engineering and Computer Science and Mathematics, Università degli Studi dell’Aquila（阿奎拉大学工程、计算机科学与数学系）；Istituto di Astrofisica e Planetologia Spaziali, INAF（INAF空间天体物理学与行星科学研究所）；Istituto Nazionale di Geofisica e Vulcanologia（国家地球物理与火山学研究所）
