Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation

Zheng Jian BAI*, Raymond H. CHAN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

20 Citations (Scopus)

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 languageEnglish
Pages (from-to)309-318
Number of pages10
JournalTheoretical Computer Science
Volume315
Issue number2-3
DOIs
Publication statusPublished - 6 May 2004
Externally publishedYes

Keywords

  • Centroskew matrix
  • Centrosymmetric matrix
  • Eigenproblem

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