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Abstract In this paper, to solve the large indefinite least squares problem, we first rewrite the normal equation of it as the sparse block three-by-three linear systems with non-singular diagonal blocks, then GMRES method is used to solve the linear systems. In order to make GMRES method converge quickly, a block upper triangular preconditioner is deduced. Theoretically, the iteration method under the preconditioner is unconditional convergent. Furthermore, the all eigenvalues of the preconditioned matrix are real number and located in a positive interval. Numerical results are provided to support the validity of the theoretical results and demonstrate the effectiveness of the studied precondition. Mathematics Subject Classification (2010) 65F10 · 65F20
Li et al. (Thu,) studied this question.