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 http://waset.org/publications/3805
http://waset.org/publications/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 ∈ 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
International Science Index 43, 2010