Yongxin Yuan Generalized Inverse Eigenvalue Problems for Symmetric Arrowhead Matrices
905 - 908
2010
4
7
International Journal of Mathematical and Computational Sciences http://waset.org/publications/6781
http://waset.org/publications/43
World Academy of Science, Engineering and Technology
In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP) Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial realvalued symmetric arrowhead matrices A and B such that AXΛ BX. We then consider an optimal approximation problem Given realvalued symmetric arrowhead matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 Bˆ − B˜2 min(A,B)∈SE (A−A˜2 B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.
International Science Index 43, 2010