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Some transpose-free CG-like solvers for nonsymmetric ill-posed problems. (English) Zbl 1441.65046
The paper is focused on iterative regularization methods for solving large square invertible linear systems \(Ax=b\), and proposes an efficient and reliable strategy to symmetrize the coefficient matrix of system. In this respect, after \(m\) iterations of the Arnoldi algorithm applied to the system, the initial problem is replaced with a preconditioned symmetric \(m\)-rank problem which is solved in the least squares sense. Numerical experiments and comparisons with other methods are presented.
MSC:
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F10 Iterative numerical methods for linear systems
65F08 Preconditioners for iterative methods
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