Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations

2008 ◽  
Vol 47 (1) ◽  
pp. 95-107 ◽  
Author(s):  
V. Kanwar ◽  
Sukhjit Singh ◽  
S. Bakshi
Keyword(s):  
Nonlinear Equations ◽  
Geometric Constructions ◽  
Iterative Functions

scholarly journals On the dynamics of a family of third-order iterative functions

2007 ◽  
Vol 48 (3) ◽  
pp. 343-359 ◽  
Author(s):  
Sergio Amat ◽  
Sonia Busquier ◽  
Sergio Plaza
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Conjugacy Classes ◽  
Complex Polynomials ◽  
Third Order ◽  
Iterative Functions

AbstractWe study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.

scholarly journals Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Ramandeep Behl ◽  
V. Kanwar ◽  
Kapil K. Sharma
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Third Order ◽  
Chebyshev’S Method ◽  
Straight Line ◽  
Special Cases ◽  
Multipoint Iterative Methods ◽  
Order Four ◽  
Square Root Method ◽  
Iterative Functions

We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain well-known methods as special cases, for example, Halley's method, super-Halley method, Ostrowski's square-root method, Chebyshev's method, and so forth. Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods. Furthermore, a simple linear combination of two third-order multipoint iterative methods is used for designing new optimal methods of order four.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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