The solvability conditions for inverse eigenproblem of symmetric and anti-persymmetric matrices and its approximation

Numerical Linear Algebra with Applications

Volumn 10, Issue 3, 2003, Pages 223-234

  Xie, Dongxiu ^a   Hu, Xiyan ^b   Zhang, Lei ^c  

^a BEIJING INSTITUTE OF MACHINERY   (China)

^b HUNAN UNIVERSITY   (China)

^c Hunan Computing Center   (China)

Author keywords

Eigenproblem; Matrix norm; The optimal solution

Indexed keywords

EID: 0037259298     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.285     Document Type: Article

References (17)

1. Nian Li. A matrix inverse eigenvalue problem and its application. Linear Algebra and its Application 1997; 266:143-152.
2. Nian Li, Chu K-WE. Designing the Hopfield neural network via pole assignment. International Journal of Systems Science 1994; 25:669-681.
3. Chen Xin. Theoretical Method and its Application of Designing of Structural Dynamics in Machine. The Mechanical Industry (Chinese) Press: Beijing, 1997; 165-202.
4. Jiang Zhengxin, Lu Qishao. On optimal approximation of a matrix under spectral restriction. Mathematics Numerica Sinica 1986; 1:47-52 (in Chinese).
5. Golub GH, Van Loan CF. Matrix Computations. The Johns Hopkins University Press: Baltimore, 1989.
6. Hu XY, Zhang L, Xie DX. The solvability conditions for the inverse eigenvalue problem of bisymmetric matrices. Mathematics Numerica Sinica 1998; 20(4):410-418.
7. Allwright JC, Woodgate KG. Errata and Addendum to: Positive semidefinite matrices characterization via conical hulls and least-squares solutions of a matrix equation. SIAM Journal on Control and Optimization 1990; 28:250-251.
8. Sun JG. Least-squares solution of a class of inverse eigenvalue problems. Mathematics Numerica Sinica 1987; 9:206-216 (in Chinese).
9. Woodgate KG, Least-squares solution of F = PG over positive semidefinite symmetric P. Linear Algebra and its Application 1996; 245:171-190.
10. Wu L, Brgan Cain. The re-nonnegative definite solutions to the matrix inverse problem AX = B. Linear Algebra and its Application 1996; 236:137-146.
11. Zhang L. The approximation on the closed convex cone and its numerical application. Hunan Annals of Mathematics 1986; 6:43-48 (in Chinese).
12. Zhang L. A class of inverse eigenvalue problem for symmetric nonnegative matrices. Journal of Hunan Educational Institute 1995; 13(2):11-17 (in Chinese).
13. Zhang L. The solvability conditions for the inverse problem of symmetric nonnegative definite matrices. Mathematics Numerica Sinica 1989; 11(4):337-343 (in Chinese).
14. Liao Anping. The necessary and sufficient conditions for the solvability of a class of the matrix inverse problem. Numerical Mathematics - A Journal Chinese Universities 1998; 7(21):195-200.
15. Higham NJ. Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Application 1998; 103:103-118.
16. 2 and a matrix programming problem. Linear Algebra and its Application 1990; 131:107-123.
17. Cheney EW. Introduction to Approximation Theory. McGraw-Hill: New York, 1966.