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Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems. (English) Zbl 1083.65045
The authors analyse a class of restrictively preconditioned conjugate gradient algorithms (RPCG) for solving large sparse systems of linear equations whose coefficient matrices are symmetric and positive definite and of block two-by-two structure. After establishing the general framework of the practical RPCG methods and demonstrating its convergence, the authors describe the algebraic constructions of two special restrictive preconditioners associated with the block Jacobi and block symmetric Gauss-Seidel splittings and prove the convergence theorems of the correspondingly induced RPCG methods.

MSC:
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
65F10Iterative methods for linear systems
65F50Sparse matrices (numerical linear algebra)
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References:
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