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The Hermitian R-Conjugate Generalized Procrustes Problem
Joint Authors
Duan, Xue-Feng
Wang, Qing-Wen
Chang, Hai-Xia
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-28
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We consider the Hermitian R-conjugate generalized Procrustes problem to find Hermitian R-conjugate matrix X such that ∑k=1p∥AkX-Ck∥2 + ∑l=1q∥XBl-Dl∥2 is minimum, where Ak, Ck, Bl, and Dl (k=1,2,…,p, l=1,…,q) are given complex matrices, and p and q are positive integers.
The expression of the solution to Hermitian R-conjugate generalized Procrustes problem is derived.
And the optimal approximation solution in the solution set for Hermitian R-conjugate generalized Procrustes problem to a given matrix is also obtained.
Furthermore, we establish necessary and sufficient conditions for the existence and the formula for Hermitian R-conjugate solution to the linear system of complex matrix equations A1X=C1, A2X=C2,…,ApX=Cp, XB1=D1,…,XBq=Dq (p and q are positive integers).
The representation of the corresponding optimal approximation problem is presented.
Finally, an algorithm for solving two problems above is proposed, and the numerical examples show its feasibility.
American Psychological Association (APA)
Chang, Hai-Xia& Duan, Xue-Feng& Wang, Qing-Wen. 2013. The Hermitian R-Conjugate Generalized Procrustes Problem. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-471018
Modern Language Association (MLA)
Chang, Hai-Xia…[et al.]. The Hermitian R-Conjugate Generalized Procrustes Problem. Abstract and Applied Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-471018
American Medical Association (AMA)
Chang, Hai-Xia& Duan, Xue-Feng& Wang, Qing-Wen. The Hermitian R-Conjugate Generalized Procrustes Problem. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-471018
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-471018