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Nonlinear Uzawa methods for solving nonsymmetric saddle point problems
Yanhua Cao,Yiqin Lin,Yimin Wei 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.21 No.1-2
Abstract. In [A new nonlinear Uzawa algorithm for generalized saddle point problems, Appl. Math. Comput., 175(2006), 1432-1454], a nonlinear Uzawa algorithm for solving symmetric saddle point problems iteratively, which was defined by two nonlinear approximate inverses, was considered. In this paper, we extend it to the nonsymmetric case. For the nonsymmetric case, its convergence result is deduced. Moreover, we compare the convergence rates of three nonlinear Uzawa methods and show that our method is more ecient than other nonlinear Uzawa methods in some cases. The results of numerical experiments are presented when we apply them to Navier-Stokes equations discretized by mixed finite elements. AMS Mathematics Subject Classification : 65F10; 65F15 xy
Wei Zhao,Zhi-Gang Yuan,Yue-hong Shen,Yufan Cao,Yimin Wei,Pengcheng Xu,Wei Jian 한국전자통신연구원 2015 ETRI Journal Vol.37 No.4
This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first-order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second-order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first-order Taylor approximation to suit higher-order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first-order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal-to-noise ratio conditions, respectively.
Yixiang Ai,Dereje Gobena Alemayehu,Genwen Mao,Yaping Liang,Ran Cao,Jiale Hu,Yimin Yang,Zhiwei Ren 대한정형외과학회 2023 Clinics in Orthopedic Surgery Vol.15 No.6
Background: To evaluate the feasibility of treating odontoid fractures in the Chinese population with two cortical screws based on computed tomography (CT) scans and describe a new measurement strategy to guide screw insertion in treating these fractures. Methods: A retrospective review of cervical computed tomographic scans of 128 patients (aged 18–76 years; men, 55 [43.0%]) was performed. The minimum external transverse diameter (METD), minimum external anteroposterior diameter (MEAD), maximum screw length (MSL), and screw projection back angle (SPBA) of the odontoid process were measured on coronal and sagittal CT images. Results: The mean values of METD and MEAD were 10.0 ± 1.1 mm and 12.0 ± 1.0 mm, respectively, in men and 9.2 ± 1.0 mm and 11.0 ± 1.0 mm, respectively, in women. Both measurements were significantly higher in men (p < 0.001). In total, 87 individuals (68%) had METD > 9.0 mm that could accommodate two 3.5-mm cortical screws. The mean MSL value and SPBA range were 34.4 ± 2.9 mm and 13.5°–24.2°, respectively, with no statistically significant difference between men and women. Conclusions: The insertion of two 3.5-mm cortical screws was possible for anterior fixation of odontoid fractures in 87 patients (68%) in our study, and there was a statistically significant difference between men and women.