Generalized inverse eigenvalue problem with mixed eigendata

AbstractIn this paper we consider a generalized inverse eigenvalue problem JnX=λCnX, where Jn is a Jacobi matrix and Cn is a nonsingular diagonal matrix that may be indefinite. Let Jk be k×k leading principal submatrix of Jn. Given Cn, two vectors X2=(xk+1,xk+2,…,xn)T, Y2=(yk+1,yk+2,…,yn)T∈Rn-k, two distinct real numbers λ, μ, we construct a Jacobi matrix Jn and two vectors X1=(x1,x2,…,xk)T, Y1=(y1,y2,…,yk)T∈Rk such that JnX=λCnX, and JnY=μCnY, where X=(X1T,X2T)T and Y=(Y1T,Y2T)T. We find necessary and sufficient conditions for solvability of this problem and we give an example