Tuning the Multithreaded Interval Method for Solving Underdetermined Systems of Nonlinear Equations

2012 ◽  
pp. 467-476 ◽  
Author(s):  
Bartłomiej Jacek Kubica
Keyword(s):  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Interval Method ◽  
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
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