Search

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., 18 pages,12 figures

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., 19 pages, 3 figures

OBJECTIVE To study the water-soluble non-alkaloid chemical constituents of Corydalis yanhusuo. METHOD The 80% alcohol extracts of C. yanhusuo passed through DA201 macroporous resin. Eluted fractions were collected and passed though 732 # cation exchange resin. Water eluate was collected, dried and derived with trimethylsilane. Gas Chromatography/Mass Spectrometry and NIST 2005 library were adopted for MS/MS mass spectrogram to infer the compound structure. RESULT Sixteen compounds were tentatively identified from about fifty peaks detected by GC-MS and identified as hydroxyl and carboxyl polar compounds. CONCLUSION These sixteen compounds were found for the first time in C. yanhusuo. The results provide scientific basis for in-depth development of C. yanhusuo.