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The Mediating Morphism of the Multilinear Optimal Map

Published online by Cambridge University Press:  28 May 2015

Seak-Weng Vong ,
Xiao-Qing Jin  and
Jin-Hua Wang
Seak-Weng Vong*
Affiliation:
Department of Mathematics, University of Macau, Macao, China
Xiao-Qing Jin*
Affiliation:
Department of Mathematics, University of Macau, Macao, China
Jin-Hua Wang*
Affiliation:
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, China
*
Corresponding author. Email: swvong@umac.mo
Corresponding author. Email: xqjin@umac.mo
Corresponding author. Email: wjh@zjut.edu.cn
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Abstract

In this short note, we study a relation between the tensor product of matrices and a multilinear map defined by the optimal operator. In this particular case, the linear transform (mediating morphism) hidden in the abstract definition of the general tensor product can be determined explicitly.

Keywords

15A6947B35Optimal preconditionertensor productmultilinear mapping
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 1 , February 2014 , pp. 82 - 87
Copyright
Copyright © Global-Science Press 2014

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References

[1]Chan, R., Jin, X., and Yeung, M., The circulant operator in the Banach algebra of matrices, Linear Algebra Appl. 149, 41–53 (1991).CrossRefGoogle Scholar
[2]Chan, R. and Ng, M., Conjugate gradient methods for Toeplitz systems, SIAM Rev. 38, 427–482 (1996).Google Scholar
[3]Chan, T., An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Stat. Comput. 9, 766–771 (1988).CrossRefGoogle Scholar
[4]Cheng, C., Jin, X., Vong, S., and Wang, W., Anote on spectra of optimal and superoptimal preconditioned matrices, Linear Algebra Appl. 422, 482–485 (2007).CrossRefGoogle Scholar
[5]Ching, W., Iterative Methods for Queuingand Manufacturing Systems, Springer-Verlag, London, 2001.Google Scholar
[6]Gilliam, D., Martin, C., and Lund, J., Analytic and numerical aspects of the observation of the heat equation, Proceedings of the 26th IEEE Conference on Decision and Control, pp. 975–976, 1987.Google Scholar
[7]Greub, W., Multilinear Algebra, 2nd Edition, Springer-Verlag, New York, 1978.CrossRefGoogle Scholar
[8]Jin, X., Preconditioning Techniques for Toeplitz Systems, Higher Education Press, Beijing, 2010.Google Scholar
[9]Jin, X., A fast algorithm for block Toeplitz systems with tensor structure, Appl. Math. Comput. 73, 115–124 (1995).Google Scholar
[10]Jin, X. and Wei, Y., A survey and some extensions of T. Chan's preconditioner, Linear Algebra Appl. 428, 403–412 (2008).CrossRefGoogle Scholar
[11]Ng, M., Iterative Methods for Toeplitz Systems, Oxford University Press, Oxford, 2004.CrossRefGoogle Scholar
[12]Roman, S., Advanced Linear Algebra, 3rd Edition, Springer-Verlag, New York, 2008.Google Scholar
[13]Strang, G., A proposal for Toeplitz matrix calculations, Stud. Appl. Math., 74, 171–176 (1986).CrossRefGoogle Scholar
[14]Tyrtyshnikov, E., Optimal and super-optimal circulant preconditioners, SIAM J. Matrix Anal. Appl. 13, 459–473 (1992).CrossRefGoogle Scholar