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Generalized inverse eigenvalue problems for tridiagonal symmetric matrices

Yuan Yongxin,Jiang Jiashang(School of Mathematics and Physics,Jiangsu University of Science and Technology,Zhenjiang Jiangsu 212003,China)  
In this paper,the following least-squares problem(LSP) was considered.Given a real matrix X∈Rn×p,and a diagonal matrix Λ∈Rp×p,finding tridiagonal symmetric matrices A,B such that ‖AX-BXΛ‖=min.Furthermore,a best approximation problem(BAP) was studied.Given tridiagonal symmetric matrices ,,find, such that ‖-‖2+‖-‖2=min(A,B)∈SE(‖A-‖2+‖B-‖2),where SE was the solution set of LSP.The uniqueness of the best approximation solution(,) was proved;and then,an explicit formula for the solution was derived.
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