Abstract
Onthe base of conjugate gradient method of solving linear algebraic equations, using special transformation and approximating disposal,an iterative method is presented to solve the least squares anti-bisymmetric solution of the matrix equation AX = B. By this iterative method, for any initial anti-bisymmetric matrix, a solution can be obtained within finite iterative steps in the absence of round off errors, and the solution with least norm can be obtained by choosing a special initial matrix. In addition, the expression of its optimal approximation solution to a given matrix can be obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Meng, T.: Experimental design and decision support, Expert Systems. In: The Technology of Knowledge Management and Decision Making for the 21st Century, vol. 1. Academic Press, Leondes (2001)
Chu, K.E.: Symmetric Solution of Linear Matrix Equations by Matrix Decompositions. Linear Algebra Appl. 119, 35–55 (1989)
Zhang, X.-D., Zhang, Z.-N.: The Anti-bisymmetric Matrices Optional Approximation Solution of Matrix Equation AX=B. Math. Appl. Sin. 32, 810–818 (2009)
Sheng, Y.P., Xie, D.X.: The Solvability Conditions for the Inverse Problem of Anti-bisymmetric Matrices. Numerical Calculation and Computer Applications 2, 111–120 (2002)
Hu, X.Y., Zhang, L., Xie, D.X.: The Solvability Conditions for the Inverse Eigenvxlue Problem of Anti-bisymmetric Matrices. Math. Numer. Sin. 4, 409–418 (1998)
Zhang, L., Xie, D.X., Hu, X.Y.: The Inverse Eigenvxlue Problem of Bisymmetric Matrices on the Linear Manifola. Math. Numer. Sin. 2, 129–138 (2000)
Higham, N.J.: Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 103, 103–118 (1988)
Peng, Z.Y., Hu, X.Y., Zhang, L.: The inverse problem of bisymmetric matrices, Numer. Linear Algebra Appl. 1, 59–73 (2004)
Cheng, Y.-P., Zhang, K.-Y., Xu, Z.: Matrix Theory, pp. 337–340. Northwestern Polytechinical University Press, Xi’an (2004)
Peng, Z.Y.: Some Matrix Extension Problems and Some Matrix Equation Problems. Ph.D.Thesis. Hunan University (2003)
Xie, D.X., Zhang, L., Hu, X.Y.: The Solvability Conditions for the Inverse Problem of Bisymmetric Nonnegative Definite Matrices. J. Comput. Math. 6, 97–608 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, L., Yuan, Xj., Liu, H. (2012). An Iterative Method for the Least Squares Anti-bisymmetric Solution of the Matrix Equation AX = B . In: Zhang, Y., Zhou, ZH., Zhang, C., Li, Y. (eds) Intelligent Science and Intelligent Data Engineering. IScIDE 2011. Lecture Notes in Computer Science, vol 7202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31919-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-31919-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31918-1
Online ISBN: 978-3-642-31919-8
eBook Packages: Computer ScienceComputer Science (R0)