Abstract
In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors {xi} i=1m in Cn and a set of complex numbers {λi}i=1m, find a centrosymmetric or centroskew matrix C in Rn×n such that {xi} i=1m and {λi}i=1m are the eigenvectors and eigenvalues of C, respectively. We then consider the best approximation problem for the IEPs that are solvable. More precisely, given an arbitrary matrix B in Rn×n, we find the matrix C which is the solution to the IEP and is closest to B in the Frobenius norm. We show that the best approximation is unique and derive an expression for it.
Original language | English |
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Pages (from-to) | 309-318 |
Number of pages | 10 |
Journal | Theoretical Computer Science |
Volume | 315 |
Issue number | 2-3 |
DOIs | |
Publication status | Published - 6 May 2004 |
Externally published | Yes |
Funding
The research was partially supported by the Hong Kong Research Grant Council Grant CUHK4243/01P and CUHK DAG 2060220.
Keywords
- Centroskew matrix
- Centrosymmetric matrix
- Eigenproblem