The Formula of Generalized Singular Values of a Class of Real Matrix Pairs

SHEN Weijie; TANG Tianyu; XU Weiwei

doi:10.6054/j.jscnun.2021100

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(6): 111-114. > DOI: 10.6054/j.jscnun.2021100

SHEN Weijie, TANG Tianyu, XU Weiwei. The Formula of Generalized Singular Values of a Class of Real Matrix Pairs[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(6): 111-114. DOI: 10.6054/j.jscnun.2021100

Citation:

PDF (383 KB)

The Formula of Generalized Singular Values of a Class of Real Matrix Pairs

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

More Information

Received Date: April 01, 2021
Available Online: January 09, 2022

Graphical Abstract

Abstract

Abstract

Using the properties of doubly stochastic matrices, the analytic solutions to a class of real diagonal matrix optimization problems are obtained, and then the formula for the i-th generalized singular value of a real matrix pair is obtained from the analytic solutions. Finally, numerical examples verify the validity of the conclusion.
- real matrix pair,
- generalized singular value,
- generalized singular value decomposition,
- trace function

FullText(HTML)

References (14)

References

[1]	戴应超. 任意实矩阵的实特征值与奇异值的估计[J]. 华南师范大学学报(自然科学版), 2005(4): 11-14. doi: 10.3969/j.issn.1000-5463.2005.04.003 DAI Y C. The estimations for real eigenvalues and singular values[J]. Journal of South China Normal University(Natural Science Edition), 2005(4): 11-14. doi: 10.3969/j.issn.1000-5463.2005.04.003
[2]	VAN L C F. Generalizing the singular value decomposition[J]. SIAM Journal on Numerical Analysis, 1976, 13: 76-83. doi: 10.1137/0713009
[3]	BANDHIT S, MASAHIRO F. An efficient framework for estimating the direction of multiple sound sources using higher-order generalized singular value decomposition[J]. Sensors, 2019, 19: 1-29. doi: 10.1109/JSEN.2019.2925985
[4]	XU W W, PANG H K, LI W, et al. On the explicit expression of chordal metric between generalized singular values of Grassmann matrix pairs with applications[J]. SIAM Journal on Matrix Analysis and Applications, 2018, 39: 1547-1563. doi: 10.1137/17M1140510
[5]	ZHANG L P, WEI Y M, CHU E K. Neural network for computing GSVD and RSVD[J]. Neurocomputing, 2021, 444: 59-66. doi: 10.1016/j.neucom.2020.10.057
[6]	WEI W, ZHANG H, YANG X, et al. Randomized genera- lized singular value decomposition[J]. Communications on Applied Mathematics and Computation, 2021, 3: 137-156. doi: 10.1007/s42967-020-00061-x
[7]	刘圆圆. 一类改进的广义随机奇异值分解方法[J]. 科学技术创新, 2020(35): 32-33. doi: 10.3969/j.issn.1673-1328.2020.35.012
[8]	HUANG J Z, JIA Z X. On choices of formulations of computing the generalized singular value decomposition of a large matrix pair[J]. Numerical Algorithms, 2020, 87(2): 689-718. doi: 10.1007/s11075-020-00984-9
[9]	XU W W, GE Z H, ZHU L. Analytic solutions of a class of extended constrained matrix maximization problems[J]. Applied Mathematics and Computation, 2020, 372: 1-8. doi: 10.1016/j.amc.2020.125120
[10]	XU W W, LU Y, ZHU L. An extension of analytic solutions of a class of constrained matrix minimization pro-blems[J]. Journal of Computational and Applied Mathematics, 2020, 372: 1-12. http://www.sciencedirect.com/science/article/pii/S0377042719306764
[11]	GOLUB G H, VAN L C F. Matrix computations[M]. Baltimore: Johns Hopkins University Press, 2013.
[12]	XU W W, LI W, ZHU L, et al. The analytic solutions of a class of constrained matrix minimization and maximization problems with applications[J]. SIAM Journal on Optimization, 2019, 29: 1657-1686. doi: 10.1137/17M1140777
[13]	张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2013.
[14]	MIRSKY L. A trace inequality of John von Neumann[J]. Monatshefte für Mathematik, 1975, 79: 303-306. doi: 10.1007/BF01647331

Cited By

Get Citation

PDF

XML

Article views (451) PDF downloads (63)

Turn off MathJax

Article Contents

Abstract

References

The Formula of Generalized Singular Values of a Class of Real Matrix Pairs

Abstract

References

Catalog

Export File

Citation

Format

Content