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New Methods For Solving Algebraic Equations

Author

Listed:
  • Mircea Cirnu

    (University “Politehnica” of Bucharest)

  • Irina Badralexi

    (University “Politehnica” of Bucharest)

Abstract

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
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    Keywords

    equations;

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