Solving Optimization Problems on Hermitian Matrix Functions with Applications
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-21
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We consider the extremal inertias and ranks of the matrix expressions f(X,Y)=A3-B3X-(B3X)*-C3YD3-(C3YD3)*, where A3=A3*, B3, C3, and D3 are known matrices and Y and X are the solutions to the matrix equations A1Y=C1, YB1=D1, and A2X=C2, respectively.
As applications, we present necessary and sufficient condition for the previous matrix function f(X, Y) to be positive (negative), non-negative (positive) definite or nonsingular.
We also characterize the relations between the Hermitian part of the solutions of the above-mentioned matrix equations.
Furthermore, we establish necessary and sufficient conditions for the solvability of the system of matrix equations A1Y=C1, YB1=D1, A2X=C2, and B3X+(B3X)*+C3YD3+(C3YD3)*=A3, and give an expression of the general solution to the above-mentioned system when it is solvable.
American Psychological Association (APA)
Zhang, Xiang& Xiang, Shu-Wen. 2013. Solving Optimization Problems on Hermitian Matrix Functions with Applications. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-483550
Modern Language Association (MLA)
Zhang, Xiang& Xiang, Shu-Wen. Solving Optimization Problems on Hermitian Matrix Functions with Applications. Journal of Applied Mathematics No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-483550
American Medical Association (AMA)
Zhang, Xiang& Xiang, Shu-Wen. Solving Optimization Problems on Hermitian Matrix Functions with Applications. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-483550
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483550