Name
Abstract | ||
|---|---|---|
Let R , S ¿ C n × n be nontrivial involutions, i.e., R = R - 1 ¿ ¿ I n and S = S - 1 ¿ ¿ I n . A matrix A ¿ C n × n is referred to as ( R , S ) -symmetric if and only if R A S = A . The set of all ( R , S ) -symmetric matrices of order n is denoted by C s n × n ( R , S ) . Given a full column rank matrix X ¿ C n × m , a matrix B ¿ C m × m and a matrix A ¿ ¿ C n × n . In structural dynamic model updating, we usually consider the sets S 1 = { A ¿ A ¿ C s n × n ( R , S ) , X H A X = B } and S 2 = { A ¿ A ¿ C s n × n ( R , S ) , ¿ X H A X - B ¿ = min } in the Frobenius norm sense, where the superscript H denotes conjugate transpose. Then we characterize the unique matrices A ¿ = arg min A ¿ S 1 ¿ A - A ¿ ¿ and A ¿ = arg min A ¿ S 2 ¿ A - A ¿ ¿ when R = R H and S = S H . By using the generalized singular value decomposition (GSVD), the necessary and sufficient conditions for the non-emptiness of S 1 and the general representations of the elements in S 1 and A ¿ are derived, respectively. The analytical expressions of A ¿ S 2 and A ¿ are also obtained by using the GSVD, the canonical correlation decomposition (CCD) and the projection theorem. Finally, a corresponding numerical algorithm and some illustrated examples are presented. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.camwa.2016.01.026 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
Inverse problem,(R,S)-symmetric matrix,Generalized singular value decomposition,Canonical correlation decomposition,Projection theorem | Generalized singular value decomposition,Rank (linear algebra),Arg max,Discrete mathematics,Combinatorics,Matrix (mathematics),Matrix norm,Symmetric matrix,Inverse problem,Mathematics,Conjugate transpose | Journal |
Volume | Issue | ISSN |
71 | 5 | 0898-1221 |
Citations | PageRank | References |
1 | 0.37 | 15 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wei-Ru Xu | 1 | 2 | 2.10 |
| Guoliang Chen | 2 | 305 | 46.48 |