Iterative solutions of generalized inverse eigenvalue problem for partially bisymmetric matrices

作者：Cai, Jing^*; Chen, Jianlong

来源：Linear and Multilinear Algebra, 2017, 65(8): 1643-1654.

DOI：10.1080/03081087.2016.1250864

• Generalized inverse eigenvalue problem
• Hermitian-Hamiltonian matrix
• submatrix constraint
• optimal approximation
• 15A29
• 65J22

In this paper, for given X. Rnxm, = diag(.1,.2,...,.m). Rmxm, an iterative algorithm is constructed to find the solutions of generalized inverse eigenvalue problem AX = BX , where A and B should be partially bisymmetric under a prescribed submatrix constraint. For any initial constrained matrices, a solution pair ( A*, B*) can be obtained in finite iteration steps by this iterative algorithm in the absence of roundoff errors. The least norm solution can be obtained by choosing a special kind of initial matrix pencil. In addition, the unique optimal approximation solution to a given matrix pencil in the solution set of the above problem can also be obtained by this iterative algorithm. Numerical examples are given to illustrate efficiency of the proposed algorithm.

• 出版日期2017
• 单位东南大学