Open Science Research Excellence
@article{(International Science Index):http://waset.org/publications/6781,
  title    = {Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices},
  author    = {Yongxin Yuan},
  country   = {China},
  institution={Hubei Normal University},
  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.
},
  {International Journal of Mathematical and Computational Sciences },  volume    = {4},
  number    = {7},
  year      = {2010},
  pages     = {905 - 908},
  ee        = {http://waset.org/publications/6781},
  url       = {http://waset.org/Publications?p=43},
  bibsource = {http://waset.org/Publications},
  issn      = {eISSN:1307-6892},
  publisher = {World Academy of Science, Engineering and Technology},
  index     = {International Science Index 43, 2010},
}