Name
Abstract | ||
|---|---|---|
Let RCmm and SCnn be nontrivial k-involutions if their minimal polynomials are both xk1 for some k2, i.e., Rk1=R1I and Sk1=S1I. We say that ACmn is (R,S,)-symmetric if RAS1=A, and A is (R,S,,)-symmetric if RAS=A with ,{0,1,,k1} and 0. Let S be one of the subsets of all (R,S,)-symmetric and (R,S,,)-symmetric matrices. Given XCnr, YCsm, BCmr and DCsn, we characterize the matrices A in S that minimize AXB2+YAD2 (Frobenius norm) under the assumption that R and S are unitary. Moreover, among the set S(X,Y,B,D)S of the minimizers of AXB2+YAD2=min, we find the optimal approximate matrix AS(X,Y,B,D) that minimizes AG to a given unstructural matrix GCmn. We also present the necessary and sufficient conditions such that AX=B,YA=D is consistent in S. If the conditions are satisfied, we characterize the consistent solution set of all such A. Finally, a numerical algorithm and some numerical examples are given to illustrate the proposed results. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.camwa.2017.02.012 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
Least squares solution,Optimal approximate solution,Moore–Penrose inverse,(R,S,μ)-symmetric matrix,(R,S,α,μ)-symmetric matrix | Combinatorics,Polynomial,System of linear equations,Matrix (mathematics),Moore–Penrose pseudoinverse,Matrix norm,Symmetric matrix,Solution set,Homogeneous space,Mathematics | Journal |
Volume | Issue | ISSN |
73 | 8 | 0898-1221 |
Citations | PageRank | References |
0 | 0.34 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wei-Ru Xu | 1 | 2 | 2.10 |
| Guoliang Chen | 2 | 305 | 46.48 |