Premium
On the low rank solution of the Q‐weighted nearest correlation matrix problem
Author(s) -
Duan XueFeng,
Bai JianChao,
Li JiaoFen,
Peng JingJing
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2027
Subject(s) - mathematics , gramian matrix , positive definite matrix , rank (graph theory) , low rank approximation , trace (psycholinguistics) , matrix (chemical analysis) , matrix norm , stationary point , quadratic equation , mathematical optimization , combinatorics , eigenvalues and eigenvectors , mathematical analysis , hankel matrix , linguistics , physics , philosophy , materials science , geometry , quantum mechanics , composite material
Summary The low rank solution of the Q‐weighted nearest correlation matrix problem is studied in this paper. Based on the property of Q‐weighted norm and the Gramian representation, we first reformulate the Q‐weighted nearest correlation matrix problem as a minimization problem of the trace function with quadratic constraints and then prove that the solution of the minimization problem the trace function is the stationary point of the original problem if it is rank‐deficient. Finally, the nonmonotone spectral projected gradient method is constructed to solve them. Numerical examples illustrate that the new method is feasible and effective. Copyright © 2015 John Wiley & Sons, Ltd.