2012Computer Engineering and Applications JournalOpen access

Interval Newton method for solving nonlinear equations with roots

Cao De-xin

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Abstract

Nonlinear equations for solving the roots are discussed,for the interval Newton method is no longer applicable and the convergence of the improved interval Newton method is so slow,by introducing a correlative equation,a new improved interval Newton method for solving the roots of nonlinear equations is established.Its local quadratic convergence property is proved,numerical examples are given.That the new method has faster convergence speed than the improved interval Newton method is verified,and it is effective and reliable.

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What this paper is about

Nonlinear equations for solving the roots are discussed,for the interval Newton method is no longer applicable and the convergence of the improved interval Newton method is so slow,by introducing a correlative equation,a new improved interval Newton method for solving the roots of nonlinear equations is established.Its local quadratic convergence property is proved,numerical examples are given.That the new method has faster convergence speed than the improved interval Newton method is verified,and it is effective and reliable.

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Available abstract

Nonlinear equations for solving the roots are discussed,for the interval Newton method is no longer applicable and the convergence of the improved interval Newton method is so slow,by introducing a correlative equation,a new improved interval Newton method for solving the roots of nonlinear equations is established.Its local quadratic convergence property is proved,numerical examples are given.That the new method has faster convergence speed than the improved interval Newton method is verified,and it is effective and reliable.

Key concepts: Newton's method, Local convergence, Mathematics, Interval (graph theory), Nonlinear system, Convergence (economics), Steffensen's method, Newton's method in optimization

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