On the generalized inverse eigenvalue problem of constructing symmetric pentadiagonal matrices from three mixed eigendata
Mahsa R. Moghaddam, Hanif Mirzaei, Kazem Ghanbari · Linear and Multilinear Algebra · 2014
In this paper, we consider a generalized inverse eigenvalue problem of the form , where and are both pentadiagonal matrices. We propose an algorithm for reconstructing a pentadiagonal matrix . Let be leading principal submatrix of . Given , a pentadiagonal matrix , distinct real numbers , , and real vectors , , , where , we construct pentadiagonal matrix and three vectors , and such that is leading principal submatrix of and , and are eigenpairs of , where , and . Sufficient conditions for solvability of the problem are given.