ABSTRACT: An n×n matrix A is said to be M-symmetric if xT(A−AT)=0 for all x∈R(M), where M∈Rn×p is given. In this paper, by extending the idea of the conjugate gradient least squares (CGLS) method, we construct an iterative method for solving a generalized inverse eigenvalue problem: minimizing ‖XTAX−C‖ where ‖⋅‖ is the Frobenius norm, X∈Rn×m and C∈Rm×m are given, and A∈Rn×n is a M-symmetric matrix to be solved. Our algorithm produces a suitable A such that XTAX=C within finite iteration steps in the absence of roundoff errors, if such an A exists. We show that the algorithm is stable any case, and we give results of numerical experiments that support this claim.
Mathematical and Computer Modelling.