On the dynamics of some Newton's type iterative functions

2009 ◽  
Vol 86 (4) ◽  
pp. 631-639 ◽  
Author(s):  
S. Amat ◽  
C. Bermúdez ◽  
S. Busquier ◽  
P. Leauthier ◽  
S. Plaza
Keyword(s):  
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.

Multistep schemes for one-point optimal iterative functions

1975 ◽  
Vol 3 (5) ◽  
Author(s):  
R. Bartłomiejczyk ◽  
S. Łanowy
Keyword(s):  
Iterative Functions

Tacoma Shuffle

1998 ◽  
Vol 91 (3) ◽  
pp. 212-216
Author(s):  
Lyman S. Holden ◽  
Loyce K. Holden
Keyword(s):  
Problem Solving ◽  
Mathematical Induction ◽  
Computer Application ◽  
Trial And Error ◽  
C Language ◽  
Key Concepts ◽  
Proof By Induction ◽  
Iterative Functions

The key concepts discussed in this article include problem-solving activities, mathematical induction, proof by induction, and use of the phrase “without loss of generality.” Several problem-solving tools are illustrated, such as trial and error, working backward, and seeing patterns. The computer application illustrates recursive and iterative functions using C language.

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