TY - JFULL
AU - Yongxin Yuan and Hao Liu
PY - 2010/8/
TI - The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
T2 - International Journal of Mathematical and Computational Sciences
SP - 860
EP - 865
VL - 4
SN - 1307-6892
UR - https://publications.waset.org/pdf/3805
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 43, 2010
N2 - 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
ER -