205
Views
6
CrossRef citations to date
0
Altmetric
Research Article

An efficient method for least-squares problem of the quaternion matrix equation X - AX̂B = C

, , &
Pages 2569-2581 | Received 24 Feb 2020, Accepted 30 Jul 2020, Published online: 20 Aug 2020

References

  • Liu JZ, Huang ZH, Zhu L, et al. Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems. Linear Algebra Appl. 2011;435:3085–3100.
  • Wang QW, van der Woude JW, Chang HX. A system of real quaternion matrix equations with applications. Linear Algebra Appl. 2009;431:2291–2303.
  • Wu AG, Feng G, Duan GR, et al. Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation. Appl Math Comput. 2011;217:4427–4438.
  • Xia JW, Chen GL, Sun W. Extended dissipative analysis of generalized Markovian switching neural networks with two delay components. Neurocomputing. 2017;260:275–283.
  • Xia JW, Gao H, Liu MX, et al. Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems. J Franklin Inst. 2018;355:3031–3049.
  • Zhang FX, Li Y, Guo WB, et al. Least squares solutions with special structure to the linear matrix equation AXB = C. Appl Math Comput. 2011;217:10049–10057.
  • Zhang FX, Li Y, Zhao JL. Common Hermitian least squares solutions of matrix equations A1XA1∗=B1 and A2XA2∗=B2 subject to inequality restrictions. Comput Math Appl. 2011;62:2424–2433.
  • Zhang FX, Wei MS, Li Y, et al. The minimal norm least squares Hermitian solution of the complex matrix equation AXB + CXD = E. J Franklin Inst. 2018;355:1296–1310.
  • Zhang FX, Wei MS, Li Y, et al. An efficient method for special least squares solution of the complex matrix equation (AXB,CXD)=(E,F). Comput Math Appl. 2018;76:2001–2010.
  • Zhang HM. Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications. Comput Math Appl. 2015;70:2049–2062.
  • Adler SL. Scattering and decay theory for quaternionic quantum mechanics, and structure of induced T nonconservation. Phys Rev D. 1988;37:3654–3662.
  • Bihan NL, Sangwine SJ. Color image decomposition using quaternion singular value decomposition. Proceedings of the International Conference on Visual Information Engineering IET; Guildford, UK. 2004.
  • Caccavale F, Natale C, Siciliano B, et al. Six-Dof impedance control based on angle/axis representations. IEEE Trans Robot Autom. 1999;15:289–300.
  • Farenick DR, Pidkowich BAF. The spectral theorem in quaternions. Linear Algebra Appl. 2003;371:75–102.
  • Ji P, Wu HT. A closed-form forward kinematics solution for the 6-6P Stewart platform. IEEE Trans Robot Autom. 2001;17:522–526.
  • Moxey CE, Sangwine SJ, Ell TA. Hypercomplex correlation techniques for vector imagines. IEEE Trans Signal Process. 2003;51:1941–1953.
  • Song GJ, Wang QW, Yu SW. Cramer's rule for a system of quaternion matrix equations with applications. Appl Math Comput. 2018;336:490–499.
  • Wang QW, He ZH, Zhang Y. Constrained two-sided coupled Sylvester-type quaternion matrix equations. Automatica. 2019;101:207–213.
  • Yuan SF, Liao AP. Least squares solution of the quaternion matrix equation X−AXˆB=C with the least norm. Linear Multilinear Algebra. 2011;59:985–998.
  • Yuan SF, Liao AP, Yao GZ. The matrix nearness problem associated with the quaternion matrix equation AXAH+BYBH=C. J Appl Math Comput. 2011;37:133–144.
  • Zhang FX, Mu WS, Li Y, et al. Special least squares solutions of the quaternion matrix equation AXB + CXD = E. Comput Math Appl. 2016;72:1426–1435.
  • Zhang FX, Wei MS, Li Y, et al. Special least squares solutions of the quaternion matrix equation AX = B with applications. Appl Math Comput. 2015;270:425–433.
  • Zhang Y, Wang RH. The exact solution of a system of quaternion matrix equations involving η-Hermicity. Appl Math Comput. 2013;222:201–209.
  • Calvetti D, Levenberg N, Reichel L. Iterative methods for X−AXB = C. J Comput Appl Math. 1997;86:73–101.
  • Jiang TS, Wei MS. On a solution of the quaternion matrix equation X−AXB = C and its application. Acta Math Sin Engl Ser. 2005;21:483–490.
  • Lancaster P, Lerer L, Tismenetsky M. Factored forms for solutions of AX−XB = C and X−AXB = C in companion matrices. Linear Algebra Appl. 1984;62:19–49.
  • Song CQ, Chen GL, Liu QB. Explicit solutions to the quaternion matrix equations X−AXF = C and X−AXF = C. Int J Comput Math. 2012;89:890–900.
  • Song CQ, Wang XD, Zhang XY. On solutions of the generalized Stein quaternion matrix equation. J Appl Math Comput. 2013;43:115–131.
  • Thiran JP, Matelart M, Le Bailly B. On the generalized ADI method for the matrix equation X−AXB = C. J Comput Appl Math. 2003;156:285–302.
  • Wu AG, Wang HQ, Duan GR. On matrix equations X−AXF = C and X−AX¯F=C. J Comput Appl Math. 2009;230:690–698.
  • Golub GH, Van Loan CF. Matrix computations. 4th ed. Baltimore (MD): The Johns Hopkins University; 2013.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.