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276 results on '"Xing, Lili"'

1. Kaczmarz-Type Methods for Solving Matrix Equations

Author

Li, Weiguo, Bao, Wendi, Xing, Lili, and Guo, Zhiwei

Subjects
Mathematics - Numerical Analysis, 65F10, 65F20, 65F30, 65F50
Abstract

In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices., Comment: arXiv admin note: text overlap with arXiv:2305.16684

Published
2023

2. A class of pseudoinverse-free greedy block nonlinear Kaczmarz methods for nonlinear systems of equations

Author

Lv, Ying, Bao, Wendi, Xing, Lili, and Li, Weiguo

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper, we construct a class of nonlinear greedy average block Kaczmarz methods to solve nonlinear problems without computing the Moore-Penrose pseudoinverse. This kind of methods adopts the average technique of Gaussian Kaczmarz method and combines with the greedy strategy, which greatly reduces the amount of computation. The convergence analysis and numerical experiments of the proposed method are given. The numerical results show the effectiveness of the proposed methods.

Published
2023

41. Progress in Ski Jumping Technology Based on Biomechanical Sport Research Methods.

Author

Li, Yuan, Liu, Lijuan, Xing, Lili, Chai, Jianzhong, and Sun, Dong

Subjects
HUMAN kinematics, MOTION, GLOBAL Positioning System, COMPUTATIONAL fluid dynamics, DRAG reduction, WIND tunnels, FLUID mechanics
Abstract

(1) Background: Previous studies have compared research into ski jumping in different motor processes, but there is a lack of comparative analysis of the biomechanical research methods used to investigate different ski jumping sports. (2) Content: Our study compared the advantages and disadvantages of six research methods and proposes future research directions. Motion video collection and analysis show that controlling angular momentum and achieving stable flight attitude in the take-off process are the most critical factors in ski jumping performance. Most research on force platforms focuses on dynamic performance at the time of take-off, but there are few training sites with an embedded force platform, and so, more empirical research is required. Wearable inertial measurement units, including gyroscopes and accelerometers, can be used to determine a series of forces, calculate the joint angle, and speculate the position of the centroid during motion. Surface EMG studies are primarily used to compare the activity characteristics of the lower limb muscles in the actual field of the jump, the exercise simulation, and the lack of complete training process data. Wind tunnel measurement can satisfy fluid mechanics simulation experiments and provide theoretical support for optimizing special ski jumping technology. Based on the theory of computational fluid dynamics, the optimal drag reduction posture data of ski jumpers can be derived using computer simulations. (3) Conclusions: Due to the wide range of ski jumping sports, the present research focused on the kinematics and dynamics of different movement stages, lacking the study of the complete exercise training process. The range of wearable inertial measurement and sensor equipment can cover the whole process of ski jumping, including kinematics and dynamics data, and is a feasible and reliable test method for monitoring ski jump training in natural environments. The simultaneous testing of surface electromyography, kinematics, and dynamics requires further exploration. (4) Future direction of development: Under computational fluid dynamics, wearable inertial measurement units and global navigation satellite systems (GNSSs), intelligent wind tunnel experimental training areas will become essential tools for ski jumping research. [ABSTRACT FROM AUTHOR]

Published
2024
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