The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximation

Journal of Computational and Applied Mathematics

Volumn 197, Issue 1, 2006, Pages 44-52

  Gong, Lisha ^a   Hu, Xiyan ^a   Zhang, Lei ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Anti symmetric matrix; Frobenius norm; Linear constraint; Optimal approximation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; LINEAR ALGEBRA; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING;

ANTI-SYMMETRIC MATRICES; FROBENIUS NORMS; LINEAR CONSTRAINTS; OPTIMAL APPROXIMATION;

MATRIX ALGEBRA;

EID: 33747035892     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.10.021     Document Type: Article

References (16)

1. * = B. Linear and Multilinear Algebra 16 (1984) 133-139
2. Dai H., and Peter L. Linear matrix equations from an inverse problem of vibration theory. Linear Algebra Appl. 246 (1996) 31-47
3. Deift P., and Nanda T. On the determination of a tridiagonal matrix from its spectrum and a submatrix. Linear Algebra Appl. 60 (1984) 43-55
4. Higham N.J. Computing a nearest symmetric positive semidefinite matrix. Linear Algebra Appl. 103 (1988) 103-118
5. Hochstadt H. On the construction of a Jacobi matrix from mixed given data. Linear Algebra Appl. 28 (1979) 113-115
6. T XA = D in bysymmetric matrix set. Math. Numer. Sinica. 24 (2002) 9-20
7. Paige C.C., and Saunders M.A. Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18 (1981) 398-405
8. Peng Z.Y. Solvability conditions for the inverse problem of real matrices with a submatrix constraint. J. Hunan Agricultural University (Natural Sciences) 6 (2001) 491-493
9. Peng Z.Y., and Hu X.Y. Constructing Jacobi Matrices with prescribed ordered defective eigenpairs and a principle submatrix. J. Comput. Appl. Math. 175 (2005) 321-333
10. T XA = B and its optimal approximation. Numer. Math. A J. Chinese Univ. 25 (2003) 372-377
11. Peng Z.Y., Hu X.Y., and Zhang L. The inverse problem of centrosymmetric matrices with a submatrix constraint. J. Comput. Math. 4 (2004) 535-544
12. Peng Z.Y., Hu X.Y., and Zhang L. The inverse problem of bisymmetric matrices with a submatrix constraint. Numer. Linear Algebra Appl. 11 (2004) 59-73
13. Penrose R. On best approximate solutions of linear matrix equation. Proc. Cambridge Philos. Soc. 52 (1956) 17-19
14. Yuan Y.X. On the two classes of best approximation problems. Math. Numer. Sinica. 23 (2001) 429-436
15. Yuan Y.X. The optimal solution of linear matrix equation by matrix decompositions. Math. Numer. Sinica. 24 (2002) 165-176
16. Zhou S.Q., and Dai H. The Algebraic Inverse Eigenvalue Problem (1991), Henan Science and Technology Press, China