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


  • Giovanni Fasano

    () (Department of Applied Mathematics, University of Venice)


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.

Suggested Citation

  • Giovanni Fasano, 2008. "Notes on a 3-term Conjugacy Recurrence for the Iterative Solution of Symmetric Linear Systems," Working Papers 179, Department of Applied Mathematics, Universit√† Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:179

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    References listed on IDEAS

    1. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    2. Amaro de Matos, Joao & Dilao, Rui & Ferreira, Bruno, 2006. "The exact value for European options on a stock paying a discrete dividend," MPRA Paper 701, University Library of Munich, Germany.
    3. M. H. Vellekoop & J. W. Nieuwenhuis, 2006. "Efficient Pricing of Derivatives on Assets with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 265-284.
    4. Geske, Robert, 1981. "Comments on Whaley's note," Journal of Financial Economics, Elsevier, vol. 9(2), pages 213-215, June.
    5. Antonella Basso & Martina Nardon & Paolo Pianca, 2004. "A two-step simulation procedure to analyze the exercise features of American options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 35-56, August.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    More about this item


    Iterative methods; 3-term recurrences; Conjugate Gradient method; Error Analysis; Preconditioning;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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