The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
| Main Authors: | Yongxin Yuan, Hao Liu |
|---|---|
| Format: | Article |
| Bahasa: | eng |
| Terbitan: |
, 2010
|
| Online Access: |
https://zenodo.org/record/1330987 |
Daftar Isi:
- 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