对称正交对称矩阵的广义特征值反问题

Inverse Generalized Eigenvalue Problem for Symmetric Orthogonal Symmetric Matrices

ZHOU Shuo^1,2, WU Bai-sheng¹

(1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2.Department of Mathematics and Physics, Northeast China Institute of Electric Power Engineering, Jilin 132012, Jilin Province, China)

Received:2005-04-08 Revised:1900-01-01 Online:2006-03-26 Published:2006-03-26
Contact: WU Bai-sheng

Abstract

Abstract: Given matrix X and diagonal matrix Λ, the solutions (A,B) of the symmetric orthogonal symmetric matrices for inverse generalized eigenvalue problem AX=BXΛ are discussed. Based on singular values decomposition of a matrix, the general form of such solutions is established. Numerical examples were presented to illus trate the validity of the proposed method.

Key words: generalized eigenvalue, inverse problem, symmetric orthogonal symmetric matrix, singular value decomposition

CLC Number:

O241.6

ZHOU Shuo, WU Bai-sheng. Inverse Generalized Eigenvalue Problem for Symmetric Orthogonal Symmetric Matrices[J].J4, 2006, 44(02): 185-188.

[1]	YIN Weishi, LIU Xiaoqi, XU Xuan. Bayesian Genetic Algorithm for Heat Source Parameter Identification Problem [J]. Journal of Jilin University Science Edition, 2020, 58(4): 841-846.
[2]	YIN Weishi, LI Jiaqi. Inverse Problem of Heat Source Identification Based onBayesianDifferential Evolution Algorithm#br# [J]. Journal of Jilin University Science Edition, 2019, 57(3): 517-522.
[3]	CHAO Yan, WANG Shibing, WANG Huiling. Image Watermarking Algorithm Based on Singular Value Decomposition and Particle Swarm Optimization Algorithm#br# [J]. Journal of Jilin University Science Edition, 2018, 56(5): 1163-1169.
[4]	ZHU Jianzhong, YAO Zhiqiang. Blind Watermarking Algorithm for Color ImagesBased on DWT-SVD and Turbo Codes [J]. Journal of Jilin University Science Edition, 2014, 52(04): 773-778.
[5]	WANG Limin, JI Qiang, HAN Xuming, HUANG Na. Selfadaptive Affinity Propagation Clustering AlgorithmBased on Singular Value Decomposition [J]. Journal of Jilin University Science Edition, 2014, 52(04): 753-757.
[6]	ZHOU Shuo, HAN Minghua, JI Benming. Inverse Generalized Eigenvalue Problem for GeneralizedReflexive Matrices under a Submatrix Constraint [J]. Journal of Jilin University Science Edition, 2013, 51(06): 1029-1036.
[7]	GUO Li-Jie, ZHOU Shuo. Optimal Approximation and Symmetric Solutions of Matrix-Inverse Problem [J]. J4, 2012, 50(06): 1075-1080.
[8]	ZHOU Shuo, YANG Shi-Tong, JIANG Zhen. A Vibration Inverse Problem of StarLike Spring Mass System [J]. J4, 2010, 48(06): 946-949.
[9]	GUO Lijie, ZHOU Shuo. Symmetric and Skew Antisymmetric Solution of \|InverseQuadratic Eigenvalue Problem and Its Optimal Approximation [J]. J4, 2009, 47(6): 1185-1190.
[10]	LIU Yuan-Yuan, ZHANG Ran. Dynamical Systems Method for Solving Inverse Problems [J]. J4, 2009, 47(05): 916-920.
[11]	DUAN Jin, JIANG Huilin, YANG Wenbo, WANG Xiaoman. Study on the Singular Value Decomposition onLaser Beam Quality Measure [J]. J4, 2009, 47(03): 594-599.
[12]	XU Xiangli, ZHANG Libiao, YU Zhezhou, ZHOU Chunguang. Image Retrieval Algorithm Based on DCT and SVD [J]. J4, 2008, 46(06): 1125-1130.
[13]	ZHOU Shuo. Inverse Problem for the Vibrating Beamfrom Its Defective Eigenpair [J]. J4, 2008, 46(04): 655-657.
[14]	XU Xiangli, ZHOU Chunguang, YU Zhezhou, ZHANG Libiao. Color Image Retrieval Algorithm in Fractal Domains [J]. J4, 2006, 44(06): 135-138.

Inverse Generalized Eigenvalue Problem for Symmetric Orthogonal Symmetric Matrices

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Metrics

Comments

Recommended 10