@article{(Open Science Index):https://publications.waset.org/pdf/3805,
	  title     = {The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation},
	  author    = {Yongxin Yuan and  Hao Liu},
	  country	= {},
	  institution	= {},
	  abstract     = {In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw
},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {4},
	  number    = {7},
	  year      = {2010},
	  pages     = {861 - 865},
	  ee        = {https://publications.waset.org/pdf/3805},
	  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},
	}