Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-19T22:20:52.839Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of iteration methods for the matrix equation A×B = C

Published online by Cambridge University Press:  17 April 2009

Konghua Guo ,
Xiyan Hu  and
Lei Zhang
Konghua Guo
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, Peoples Republic of China, e-mail: khguo@126.com
Xiyan Hu
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, Peoples Republic of China, e-mail: khguo@126.com
Lei Zhang
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, Peoples Republic of China, e-mail: khguo@126.com
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An iteration method for the matrix equation A×B = C is constructed. By this iteration method, the least-norm solution for the matrix equation can be obtained when the matrix equation is consistent and the least-norm least-squares solutions can be obtained when the matrix equation is not consistent. The related optimal approximation solution is obtained by this iteration method. A preconditioned method for improving the iteration rate is put forward. Finally, some numerical examples are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 289 - 298
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Bjerhammer, A., ‘Rectangular reciprocal matrices with special reference to geodetic calculations’, Kung. Tekn. Hogsk. Handl. Stockhol 45 (1951).Google Scholar
[2]Chu, K-W.E., ‘Symmetric solutions of linear matrix equations by matrix decompositions’, Linear Algebra Appl. 119 (1989), 35–50.CrossRefGoogle Scholar
[3]Dai, H., ‘On the symmetric solutions of linear matrix equations’, Linear Algebra Appl. 131 (1990), 1–7.Google Scholar
[4]Don, F.J.H, ‘On the symmetric solution of a linear matrix equation’, Linear Algebra Appl. 93 (1987), 1–7.Google Scholar
[5]Li, G., Common matrix theries and methods (Shanghai Science and Technology Press, Shanghai 1983).Google Scholar
[6]Magnus, J.R., ‘L-structured matrices and linear matrix equation’, Linear and Multilinear Algebra 14 (1983), 67–88.CrossRefGoogle Scholar
[7]Mitra, S.K., ‘Common solutions to a pair of linear matrix equations A 1×B 1 = C 1 and A2×B2 = C2, Proc.Cambridge Philos. Soc. 74 (1973), 213–216.CrossRefGoogle Scholar
[8]Morris, G.R. and Odell, P.L., ‘Common solutions for n matrix equations with applications’, J. Assoc. Comput. Mach. 15 (1968), 272–274.CrossRefGoogle Scholar
[9]Peng, Y.X. and Hu, X.Y., ‘An iteration method for the symmetric solutions and optimal approximation solution of the matrix equation A×B = C’ Appl. Math. Comput. 160 (2005), 163–167.Google Scholar
[10]Penrose, R., ‘A generalized inverse for matricies’, Proc. Cambridge Philos. Soc. 5 (1955), 406–413.CrossRefGoogle Scholar
[11]He, X.C. and Sun, W.Y., Introduction to generalized inverse of matrices (Jiangsu Science and Technology Press, Nanjing, 1991).Google Scholar