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Abstract In this paper, we construct a circulant-matrix-based new accelerated GSOR (CNAGSOR) iteration method for a class of large and sparse block two-by-two linear systems of generalized saddle-point structure. Theoretical… Click to show full abstract
Abstract In this paper, we construct a circulant-matrix-based new accelerated GSOR (CNAGSOR) iteration method for a class of large and sparse block two-by-two linear systems of generalized saddle-point structure. Theoretical results about the convergence properties and eigenvalues distribution of the preconditioning matrix are studied in detail. Implementations in the image restoration problem and in the PDE-constraint optimization problem are made to verify the feasibility and the efficiency of the new methods.
Journal Title: Applied Numerical Mathematics
Year Published: 2021
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