Finding all real roots of 3×3 nonlinear algebraic systems using neural networks

2013 ◽  
Vol 219 (9) ◽  
pp. 4444-4464 ◽  
Author(s):  
Konstantinos Goulianas ◽  
Athanasios Margaris ◽  
Miltiades Adamopoulos
Keyword(s):  
Neural Networks ◽  
Algebraic Systems ◽  
Real Roots ◽  
Nonlinear Algebraic Systems

scholarly journals Application of a subdivision algorithm for solving nonlinear algebraic systems

2008 ◽  
Vol 30 (1) ◽  
Author(s):  
Fernanda De Castilhos Corazza ◽  
José Vladimir de Oliveira ◽  
Marcos Lúcio Corazza
Keyword(s):  
Algebraic Systems ◽  
Nonlinear Algebraic Systems ◽  
Subdivision Algorithm

A Simple Iterative Solution of Nonlinear Algebraic Systems

2009 ◽  
Author(s):  
Maria Gousidou ◽  
Christopher Koutitas ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Iterative Solution ◽  
Algebraic Systems ◽  
Nonlinear Algebraic Systems

The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator

1988 ◽  
Vol 110 (1) ◽  
pp. 35-41 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Numerical Methods ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Design Criteria ◽  
Algebraic Systems ◽  
Kinematic Design ◽  
Nonlinear Algebraic Systems ◽  
Global Workspace ◽  
Three Degree Of Freedom

In this paper, the design of a planar three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Four different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) the existence of a nonvanishing workspace for every orientation of the gripper (c) the maximization of the global workspace, and (d) the isotropy of the Jacobian of the manipulator. The four associated problems are formulated and their solutions are derived. Two of these require to resort to numerical methods for nonlinear algebraic systems. Results of optimum designs are also included.

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