Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4639922 | Journal of Computational and Applied Mathematics | 2011 | 8 Pages |
Abstract
In this paper, we first give the representation of the general solution of the following inverse monic quadratic eigenvalue problem (IMQEP): given matrices Î=diag{λ1,â¦,λp}âCpÃp, λiâ λj for iâ j, i,j=1,â¦,p, X=[x1,â¦,xp]âCnÃp, rank(X)=p, and both Î and X are closed under complex conjugation in the sense that λ2j=λÌ2jâ1âC, x2j=xÌ2jâ1âCn for j=1,â¦,l, and λkâR, xkâRn for k=2l+1,â¦,p, find real-valued symmetric matrices D and K such that XÎ2+DXÎ+KX=0. Then we consider a best approximation problem: given DÌ,KÌâRnÃn, find (DË,KË)âSDK such that â(DË,KË)â(DÌ,KÌ)âW=min(D,K)âSDKâ(D,K)â(DÌ,KÌ)âW, where ââ
âW is a weighted Frobenius norm and SDK is the solution set of IMQEP. We show that the best approximation solution (DË,KË) is unique and derive an explicit formula for it.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yongxin Yuan, Hua Dai,