IDEAS home Printed from
   My bibliography  Save this article

New Methods For Solving Algebraic Equations


  • Mircea Cirnu

    (University “Politehnica” of Bucharest)

  • Irina Badralexi

    (University “Politehnica” of Bucharest)


Iteration methods are very useful in solving nonlinear algebraic equations. The most famous such method is Newton’s method deduced by first order Taylor expansion. In 2003, J. H. He gives a new faster convergent method, based on second order Taylor expansion, that gives a quadratic equation for the iterations difference xn+1-xn . However He’s method is not applicable when this equation has complex roots. In 2008, D. Wei, J. Wu and M. Mei eliminated this deficiency, obtaining from third order Taylor expansion a cubic equation, that always has a real root. In this paper, we present the three methods and their applications to some particular equations.

Suggested Citation

  • Mircea Cirnu & Irina Badralexi, 2010. "New Methods For Solving Algebraic Equations," Romanian Economic Business Review, Romanian-American University, vol. 4(1), pages 137-140, May.
  • Handle: RePEc:rau:journl:v:4:y:2010:i:1:p:137-140

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Leitemo, Kai & Söderström, Ulf, 2008. "Robust Monetary Policy In The New Keynesian Framework," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S1), pages 126-135, April.
    2. Dennis, Richard & Leitemo, Kai & Söderström, Ulf, 2009. "Methods for robust control," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1604-1616, August.
    3. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 581-604, April.
    4. Leitemo, Kai & Söderström, Ulf, 2004. "Robust monetary policy in the New-Keynesian framework," Research Discussion Papers 31/2004, Bank of Finland.
    5. Giordani, Paolo & Soderlind, Paul, 2004. "Solution of macromodels with Hansen-Sargent robust policies: some extensions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2367-2397, December.
    6. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    7. Backus, David & Driffill, John, 1986. "The Consistency of Optimal Policy in Stochastic Rational Expectations Models," CEPR Discussion Papers 124, C.E.P.R. Discussion Papers.
    Full references (including those not matched with items on IDEAS)

    More about this item




    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rau:journl:v:4:y:2010:i:1:p:137-140. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alex Tabusca). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.