We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and we provide some error analysis. Then, we introduce preconditioning for CG_2step, and we prove that standard error bounds for the CG also hold for our proposal.

Notes on a 3-term Conjugacy Recurrence forthe Iterative Solution of Symmetric Linear Systems

FASANO, Giovanni
2008-01-01

Abstract

We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and we provide some error analysis. Then, we introduce preconditioning for CG_2step, and we prove that standard error bounds for the CG also hold for our proposal.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/19028
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