Least-squares solutions of constrained inverse eigenproblem and associated optimal approximation problem

In this paper, the least-squares solutions of constrained inverse eigenvalue problem and the associated optimal approximation problem are considered. We get the general expression of the least-squares solutions of the constrained inverse eigenvalue problem, obtain the representation of the unique optimal approximation solution in the least-squares solutions set, and give the algorithm and corresponding computational examples.

[1]  Zhang Lei,et al.  THE SOLVABILITY CONDITIONS FOR A CLASS OF CONSTRAINED INVERSE EIGENVALUE PROBLEM OF ANTISYMMETRIC MATRICES , 2006 .

[2]  W. F. Trench,et al.  Inverse Eigenproblems and Associated Approximation Problems for Matrices with Generalized Symmetry or Skew Symmetry , 2003 .

[3]  K. T. Joseph.  Inverse eigenvalue problem in structural design , 1992 .

[4]  Zhang Zhong.  Least-squares Solutions of Inverse Problems for D-symmetric Matrices , 2001 .

[5]  Xi-Yan Hu,et al.  The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations☆ , 2006 .

[6]  Chen Xing-tong.  Inverse Eigenvalue Problem of Symmetric Ortho-Symmetric Positive Semi-Definite Matrices , 2005 .

[7]  Xiyan Hu,et al.  The solvability conditions for the inverse eigenvalue problem of the symmetrizable matrices , 2004 .

[8]  Xiyan Hu,et al.  The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices☆ , 2003 .

[9]  Lei Zhang,et al.  A kind of inverse eigenvalue problems of Jacobi matrix , 2006, Appl. Math. Comput..

[10]  D. Xie,et al.  Least-squares solution for inverse eigenpair problem of nonnegative definite matrices , 2000 .

[11]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[12]  Xie,et al.  THE SOLVABILITY CONDITIONS FOR INVERSE EIGENVALUE PROBLEM OF ANTI-BISYMMETRIC MATRICES , 2002 .

[13]  Xiaoshu Pan,et al.  A class of constrained inverse eigenproblem and associated approximation problem for skew symmetric and centrosymmetric matrices , 2005 .

[14]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .