Convergence of Inner-Iteration GMRES Methods for Least Squares Problems
نویسندگان
چکیده
We develop a general convergence theory for the generalized minimal residual method for least squares problems preconditioned with inner iterations. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory is improved particularly in the rankdeficient case. We analyse the spectrum of the preconditioned coefficient matrix, and characterize it by the spectral radius of the iteration matrix for the inner iterations. The analysis is supported by numerical experiments.
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