A New ICCG Method of Large-Scale Sparse Linear Equation Group

Author(s):  
Zhang Yongjie ◽  
Sun Qin
2021 ◽  
Author(s):  
Wenjun Su ◽  
Junkang Guo ◽  
Zhigang Liu ◽  
Kang Jia

Abstract Rotary-laser automatic theodolite (R-LAT) system is a distributed large-scale metrology system, which provides parallel measurement in scalable measurement room without obvious precision losing. Each of R-LAT emits two nonparallel laser planes to scan the measurement space via evenly rotation, while the photoelectric sensors receive these laser planes signals and performs the coordinate calculation based on triangulation. The accurate geometric parameters of the two laser planes plays a crucial role in maintaining the measurement precision of R-LAT system. Practically, the geometry of the two laser plane, which is termed as intrinsic parameters, is unknown after assembled. Therefore, how to figure out the accurate intrinsic parameters of each R-LAT is a fundamental question for the application of R-LAT system. This paper proposed an easily operated intrinsic parameter calibration method for R-LAT system with adopting coordinate measurement machine. The mathematic model of laser planes and the observing equation group of R-LAT are established. Then, the intrinsic calibration is formulated as a nonlinear least square problem that minimize the sum of deviations of target points and laser planes, and the ascertain of its initial guess is introduced. At last, experience is performed to verify the effectiveness of this method, and simulations are carried out to investigate the influence of the target point configuration on the accuracy of intrinsic parameters.


2013 ◽  
Vol 404 ◽  
pp. 538-542 ◽  
Author(s):  
Rui Hong Zhou ◽  
Yue Guang Li

In this paper, according to the characteristics of ill-conditioned linear equation groups. A novel bat algorithm was used to solve the systems of ill-conditioned linear equation groups, the algorithm was experimented and the experimental results show that the novel algorithm is effective for solving ill-conditioned linear equation groups.


2018 ◽  
Vol 15 ◽  
pp. 6-11
Author(s):  
Michal Bošanský ◽  
Bořek Patzák

<p>The aim of this paper is to evaluate the performance of existing parallel linear equation solvers to solving large-scale, nonlinear finite element analysis problems on systems with distributed memory. The parallel approach allows us to take an advantage of the distributed memory enabling forming large system matrices and of multiple processing units to achieve significant speedups. Our study is based on comparison of parallel direct solver and parallel iterative solver implemented in SuperLU DIST library from Portable, Extensible Toolkit for Scientific Computation (PETSc). Both considered solvers are designed for distributed system memory model and are based on a Massage Passing Interface (MPI).</p><p>The efficiency of individual solvers is evaluated on a selected benchmark problems, with different solution strategies by comparing computation times and obtained speedups.</p>


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