scholarly journals Algorithmic Differentiation of Numerical Methods: Second-order Adjoint Solvers for Parameterized Systems of Nonlinear Equations

2016 ◽  
Vol 80 ◽  
pp. 2231-2235 ◽  
Author(s):  
Niloofar Safiran ◽  
Johannes Lotz ◽  
Uwe Naumann
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Second Order ◽  
Systems Of Nonlinear Equations ◽  
Algorithmic Differentiation ◽  
Parameterized Systems

scholarly journals Optimally rotated vectors

2003 ◽  
Vol 2003 (63) ◽  
pp. 4015-4023 ◽  
Author(s):  
Morteza Seddighin
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
Systems Of Nonlinear Equations ◽  
Real Numbers ◽  
Lagrange Multiplier Technique ◽  
The Matrix

We study vectors which undergo maximum or minimum rotation by a matrix on the field of real numbers. The cosine of the angle between a maximally rotated vector and its image under the matrix is called the cosine or antieigenvalue of the matrix and has important applications in numerical methods. Using Lagrange multiplier technique, we obtain systems of nonlinear equations which represent these optimization problems. Furthermore, we solve these systems symbolically and numerically.

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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