Yongxin Yuan and Hao Liu
The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
861 - 865
2010
4
7
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/3805
https://publications.waset.org/vol/43
World Academy of Science, Engineering and Technology
In this paper, we first give the representation of the general solution of the following leastsquares problem (LSP) Given matrices X &isin; Rn&times;p, B &isin; Rp&times;p and A0 &isin; Rr&times;r, find a matrix A &isin; Rn&times;n such that XT AX &minus; B min, s. t. A(1, r) A0, where A(1, r) is the r&times;r leading principal submatrix of the matrix A. We then consider a best approximation problem given an n &times; n matrix A&tilde; with A&tilde;(1, r) A0, find A&circ; &isin; SE such that A&tilde; &minus; A&circ; minA&isin;SE A&tilde; &minus; A, where SE is the solution set of LSP. We show that the best approximation solution A&circ; is unique and derive an explicit formula for it. Keyw
Open Science Index 43, 2010