Modified PSO Algorithm for Solving the Eigenvalues of Matrix

Abstract:

Presently, most of the PSO algorithms for eigenvalues computation take the characteristic polynomial as its fitness function, while for large matrix; it needs a lot of computation for its determination. In order to improve the efficiency of arithmetic operations, a new definition of fitness function, the fitness function calculation of which is much less than the calculation of the determination, can greatly improve the efficiency of algorithms. Finally, several different types of matrix operator cases further validate the effectiveness of the obtained results.

• Periodical: Advanced Materials Research (Volumes 846-847)
• Pages: 1316-1319
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.846-847.1316
• Online since: November 2013
• Authors: Ying Zhou*, Xia Long, Ping Liao
• Keywords: Eigenvalues, Fitness Function, Particle Swarm Optimization (PSO)

References

[1] Cao Zhihao. Eigenvalue Problems [M]. Shanghai Science and Technology Press, 1980. In Chinese.

[2] Kennedy J, Eberhart R. Particle swarms optimization[C]. /IEEE International Conference on Neural Networks, Perth, Australia, (1995).

[3] Yuan Liguo, Song Tao, Qiu, et al. Estimated eigenvalues particle swam optimization algorithm [J]. Computer Engineering and Design, 2009, 30(9): 2249-2253. In Chinese.

[4] Wei Xingqiong, Zhou Yongquan. Solving matrix eigenvalues and eigenvectors of the PSO algorithm [J]. Computer Engineering, 2010, 36(3): 189-191. In Chinese.

[5] Wang Zhi, Hu Xiaobing, He Xuehai. Solving improved PSO Algorithm of matrix eigenvalues [J]. Computer Engineering and Applications, 2012, 48 (9): 40-42. In Chinese.

[6] Zhan Xingzhi. Matrix Theory [M]. Beijing: Higher Education Press, 2008. In Chinese.

[7] Shi Y, Eberhart R. Monitoring of particle swarm optimization [J]. Frontiers of computer Science in China. 2009, 3(1): 31-37.