@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},
	}