An efficient algorithm based on Lanczos type of BCR to solve constrained quadratic inverse eigenvalue problems

This paper proposes the Lanczos type of biconjugate residual (BCR) algorithm for solving the quadratic inverse eigenvalue problem L2XΛ2+L1XΛ+L0X=0 where L2, L1 and L0 should be partially bisymmetric under a prescribed submatrix constraint. An analysis reveals that the algorithm obtains the solutions of the constrained quadratic inverse eigenvalue problem in finitely many steps in the absence of round-off errors. Finally numerical results are performed to confirm the analysis and to illustrate the efficiency of the proposed algorithm.