A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications (original) (raw)

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

1. Adler, S.: Composite leptons quark constructed as triply occupied quasi-particle in quaternionic quantum mechanics. Phys. Lett B. 332, 358–365 (1994)
   Article Google Scholar
2. Adler, S.: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, New York (1995)
   MATH Google Scholar
3. De Leo, S., Ducati, G.: Quaternionic groups in physics. Int. J. Theor. Phys. 38, 2197–2220 (1999)
   Article MathSciNet MATH Google Scholar
4. Le Bihan, N., Sangwine, S.: Quaternion principal component analysis of color images. IEEE Int. Conf. Image Process 1, 809–812 (2003)
   Google Scholar
5. Mackey, D.S., Mackey, N., Tisseur, F.: Structured tools for structured matrices. Electron. J. Linear Algebra 10, 106–145 (2003)
   Article MathSciNet MATH Google Scholar
6. Sangwine, S., Le Bihan, N.: Quaternion toolbox for matlab. http://qtfm.sourceforge.net/
7. Jiang, T.: An algorithm for quaternionic linear equations in quaternionic quantum theory. J. Math. Phys. 45(11), 4218–4222 (2004)
   Article MathSciNet MATH Google Scholar
8. Wang, G., Guo, Z., Zhang, D., Jiang, T.: Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory. Math. Meth. Appl. Sci. 43 (3), 1124–1137 (2020)
   Article MathSciNet MATH Google Scholar
9. Wang, M., Ma, W.: A structure-preserving algorithm for the quaternion Cholesky decomposition. Appl. Math. Comput. 223, 354–361 (2013)
   MathSciNet MATH Google Scholar
10. Wang, M., Ma, W.: A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory. Comput. Phys. Commun. 184(9), 2182–2186 (2013)
    Article MathSciNet MATH Google Scholar
11. Sangwine, S.J.: Comment on ‘A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory’ by Minghui Wang and Wenhao Ma. Comput. Phys. Commun. 188, 128–130 (2015)
    Article MathSciNet Google Scholar
12. Li, Y., Wei, M., Zhang, F., Zhao, J.: A real structure-preserving method for the quaternion LU decomposition, revisited. Calcolo 54(4), 1553–1563 (2017)
    Article MathSciNet MATH Google Scholar
13. Li, Y., Wei, M., Zhang, F., Zhao, J.: A fast structure-preserving method for computing the singular value decomposition of quaternion matrices. Appl. Math. Comput. 235, 157–167 (2014)
    MathSciNet MATH Google Scholar
14. Li, Y., Wei, M., Zhang, F., Zhao, J.: Real structure-preserving algorithms of Householder based transformations for quaternion matrices. Comput. Appl. Math. 305, 82–91 (2016)
    Article MathSciNet MATH Google Scholar
15. Li, Y., Wei, M., Zhang, F., Zhao, J.: On the power method for quaternion right eigenvalue problem. Comput. Appl. Math. 345, 59–69 (2019)
    Article MathSciNet MATH Google Scholar
16. Jia, Z., Wei, M., Ling, S.: A new structure-preserving method for quaternion Hermitian eigenvalue problems. Comput. Appl. Math. 239, 12–24 (2013)
    Article MathSciNet MATH Google Scholar
17. Ma, R., Jia, Z., Bai, Z.: A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems. Comput. Math. Appl. 75 (3), 809–820 (2018)
    Article MathSciNet MATH Google Scholar
18. Wei, M., Li, Y., Zhang, F., Zhao, J.: Quaternion Matrix Computations. Nova Science Publishers (2018)
19. Lu, Y., Cui, J., Fang, Z.: Enhancing sparsity via full rank decomposition for robust face recognition. Neural Comput. Appl. 25, 1043–1052 (2014)
    Article Google Scholar
20. Malkoti, A., Vedanti, N., Tiwari, R. K.: A highly efficient implicit finite difference scheme for acoustic wave propagation. J. Appl. Geophys. 161, 204–215 (2019)
    Article Google Scholar
21. Cosnard, M., Marrakchi, M., Robert, Y.: Parallel Gaussian elimination on an MIMD computer. Parallel Comput. 6, 275–296 (1988)
    Article MathSciNet MATH Google Scholar
22. Litvinov, G.L., Maslova, E.V.: Universal numerical algorithms and their software implementation. Program Comput. Software 26(5), 275–280 (2000)
    Article MathSciNet MATH Google Scholar
23. Sheng, X., Chen, G.: Full-rank representation of generalized inverse \(A^{(2)}_{{{TS}}}\) and its application, Comput. Math. Appl. 54, 1422–1430 (2007)
    Google Scholar
24. Jiang, M., Jiang, B., Cai, W., Du, X., et al.: Internal model control for structured rank deficient system based on full rank decomposition. Cluster Comput. 20, 13–24 (2017)
    Article Google Scholar

Download references