《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (2): 20-25.doi: 10.6040/j.issn.1671-9352.0.2024.392
• • 上一篇
汪秋分,马昌凤*
WANG Qiufen, MA Changfeng*
摘要: 研究*-Sylvester矩阵方程AX+X*B=D的等价转换形式。利用Kronecker积和向量化算子以及置换矩阵的基本性质,分离了矩阵的实部和虚部,在两种不同的情况下得到了*-Sylvester矩阵方程的等价转换形式,并证明了在满足一定条件下其可以等价转换为广义Sylvester矩阵方程。
中图分类号:
| [1] HOFER M, FINGER N, KOVACS G, et al. Finite-element simulation of wave propagation in periodic piezoelectric SAW structures[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2006, 53(6):1192-1201. [2] BYERS R, KRESSNER D. Structured condition numbers for invariant subspaces[J]. SIAM Journal on Matrix Analysis and Applications, 2006, 28(2):326-347. [3] DAI Liyi. Singular Control Systems[M]. Berlin: Springer-Verlag, 1989. [4] DUAN Guangren. The solution to the matrix equation AV+BW=EVJ+R[J]. Applied Mathematics Letters, 2004, 17(10):1197-1202. [5] FRANK P M. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey and some new results[J]. Automatica, 1990, 26(3):459-474. [6] CHIANG C Y, CHU E K W, LIN W W. On the ★-Sylvester equation AX±X★B★=C[J]. Applied Mathematics and Computation, 2012, 218(17):8393-8407. [7] KE Yifen, MA Changfeng. The alternating direction methods for solving the Sylvester-type matrix equation AXB+CXD=E[J]. Journal of Computational Mathematics, 2017, 35(5):620-641. [8] DE TERÁN F, DOPICO F. Consistency and efficient solution of the Sylvester equation for *-congruence[J]. The Electronic Journal of Linear Algebra, 2011, 22:849-863. [9] DE TERÁN F, IANNAZZO B. Uniqueness of solution of a generalized *-Sylvester matrix equation[J]. Linear Algebra and its Applications, 2016, 493:323-335. [10] 吴玉玲,郑佳莉,柯艺芬,等. 求解四元数矩阵方程AX+XB=C的全局拟极小残量法[J]. 山东大学学报(理学版),2025,60(12):60-74. WU Yuling, ZHENG Jiali, KE Yifen, et al. Global quasi-minimal residual method for solving quaternion matrix equation AX+XB=C[J]. Journal of Shandong University(Natural Science), 2025, 60(12):60-74. [11] ZHANG Huamin, YIN Hongcai. New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation[J]. Journal of the Franklin Institute, 2017, 354(16):7585-7603. [12] DING Feng, CHEN Tongwen. On iterative solutions of general coupled matrix equations[J]. SIAM Journal on Control and Optimization, 2006, 44(6):2269-2284. [13] DING F, PETER X L, DING J. Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle[J]. Applied Mathematics and Computation, 2008, 197(1):41-50. [14] OOZAWA M, SOGABE T, MIYATAKE Y, et al. On a relationship between the T-congruence Sylvester equation and the Lyapunov equation[J]. Journal of Computational and Applied Mathematics, 2018, 329:51-56. [15] SATAKE Y, OOZAWA M, SOGABE T, et al. Relation between the T-congruence Sylvester equation and the generalized Sylvester equation[J]. Applied Mathematics Letters, 2019, 96:7-13. [16] 马昌凤,柯艺芬,谢亚君. 广义★-Sylvester矩阵方程的重新表述[J]. 山西大学学报(自然科学版),2025,48(4):700-704 MA Changfen, KE Yifen, XIE Yajun. The reformulation of a generalized ★-Sylvester matrix equation[J]. Journal of Shanxi University(Natural Science Edition), 2025, 48(4):700-704. [17] ZHANG Huamin, DING Feng. On the Kronecker products and their applications[J]. Journal of Applied Mathematics, 2013, 1:1-8. [18] KRESSNER D, SCHRÖDER C, WATKINS D S. Implicit QR algorithms for palindromic and even eigenvalue problems[J]. Numerical Algorithms, 2009, 51(2):209-238. |
| [1] | 凌思涛 程学汉 魏木生. 一般线性四元数矩阵方程的Hermite解[J]. J4, 2008, 43(12): 1-4. |
|
||