@article{(Open Science Index):https://publications.waset.org/pdf/6781, title = {Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices}, author = {Yongxin Yuan}, country = {}, institution = {}, abstract = {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 real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head 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. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {4}, number = {7}, year = {2010}, pages = {905 - 908}, ee = {https://publications.waset.org/pdf/6781}, url = {https://publications.waset.org/vol/43}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 43, 2010}, }