A Sparse Update Method for Solving Underdetermined Systems of Nonlinear Equations Applied to the Manipulation of Biological Signaling Pathways

2012 ◽  
Vol 72 (4) ◽  
pp. 982-1001 ◽  
Author(s):  
Philipp Kuegler
Keyword(s):  
Signaling Pathways ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Underdetermined Systems

Solution method for underdetermined systems of nonlinear equations

2019 ◽  
Vol 34 (3) ◽  
pp. 163-174
Author(s):  
Ewa Szczepanik ◽  
Alexey A. Tret’yakov ◽  
Eugene E. Tyrtyshnikov
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Solution Method ◽  
Degenerate Case ◽  
Systems Of Nonlinear Equations ◽  
Underdetermined Systems

Abstract In this paper we present a new solution method for underdetermined systems of nonlinear equations in a neighborhood of a certain point of the variety of solutions where the Jacoby matrix has incomplete rank. Such systems are usually called degenerate. It is known that the Gauss–Newton method can be used in the degenerate case. However, the variety of solutions in a neighborhood of the considered point can have several branches in the degenerate case. Therefore, the analysis of convergence of the method requires special techniques based on the constructions of the theory of p-regularity and p-factor-operators.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations

Research on the Forward Kinematics of Stewart Platform Using Memetic Algorithms

2012 ◽  
Vol 268-270 ◽  
pp. 1416-1421
Author(s):  
Yu Hui Zhang ◽  
Li Wen Guan ◽  
Li Ping Wang ◽  
Yong Zhi Hua
Keyword(s):  
Nonlinear Equations ◽  
Rapid Development ◽  
Memetic Algorithms ◽  
Stewart Platform ◽  
Global Optimum ◽  
General Purpose ◽  
Forward Kinematics ◽  
Systems Of Nonlinear Equations ◽  
Artificial Intelligence Technology ◽  
Difficult Issue

The forward kinematics analysis of parallel manipulator is a difficult issue, which has been studied by many researchers recently. In this paper, in order to solve the difficult issue, a new computing method with higher calculation accuracy, good operation steadiness and faster speed is mentioned. Firstly, the mathematical model of direct kinematics of the Stewart platform is founded, which is nonlinear equations. Secondly, with the rapid development of artificial intelligence technology, Memetic algorithms (MA) are applied to solve the systems of nonlinear equations more and more, replacing the traditional algorithms. MA is a kind of meta-heuristic algorithm combined genetic algorithms (GA) with local search at the end of iteration. Finally, the validity of this algorithm has been testified by simulating iteration operation. The numerical simulation shows that MA can surely and rapidly get global optimum solution and greatly improve convergence rate. Thereby, MA can be widely used as a general-purpose algorithm for solving the forward kinematics of parallel mechanism.

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