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

Giovanni Fasano ()

No 179, Working Papers from Department of Applied Mathematics, Università Ca' Foscari Venezia

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.

Keywords: Iterative methods; 3-term recurrences; Conjugate Gradient method; Error Analysis; Preconditioning (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2008-11
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