scholarly journals A Special Homotopy Continuation Method for a Class of Polynomial Systems

2017 ◽  
pp. 362-376 ◽  
Author(s):  
Yu Wang ◽  
Wenyuan Wu ◽  
Bican Xia
Keyword(s):  
Continuation Method ◽  
Polynomial Systems ◽  
Homotopy Continuation ◽  
Homotopy Continuation Method

PHoM ? a Polyhedral Homotopy Continuation Method for Polynomial Systems

Computing ◽  
2004 ◽  
Vol 73 (1) ◽  
Author(s):  
Takayuki Gunji ◽  
Sunyoung Kim ◽  
Masakazu Kojima ◽  
Akiko Takeda ◽  
Katsuki Fujisawa ◽  
...  
Keyword(s):  
Continuation Method ◽  
Polynomial Systems ◽  
Homotopy Continuation ◽  
Polyhedral Homotopy ◽  
Homotopy Continuation Method

scholarly journals An Application of the Newton-Homotopy Continuation Method for Solving the Forward Kinematic Problem of the 3-RRS Parallel Manipulator

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Jaime Gallardo-Alvarado
Keyword(s):  
Parallel Manipulator ◽  
Continuation Method ◽  
Three Dimensional ◽  
Polynomial Systems ◽  
General Purpose ◽  
Homotopy Continuation ◽  
Homotopy Continuation Method ◽  
Forward Kinematic Problem ◽  
Forward Kinematic ◽  
Newton Homotopy

The forward kinematic problem (FKP) of the 3-RRS parallel manipulator is solved by means of the Newton-homotopy continuation method. The closure equations are formulated in the three-dimensional Euclidean spaces considering the coordinates of the centers of the spherical joints as unknown variables. The method is easy to follow and unlike the classical Newton-Raphson method it allows finding all the solutions of the FKP. A case study is included in the contribution in order to confirm the correctness of the method. In that concern, the numerical results obtained by means of the proposed method are verified with the aid of two different approaches such as the application of commercially available software like Maple16™ and the application of the PHCpack, a general purpose solver for polynomial systems based on homotopy continuation.

scholarly journals New collocation path-following approach for the optimal shape parameter using Kernel method

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Zouhair Saffah ◽  
Abdelaziz Timesli ◽  
Hassane Lahmam ◽  
Abderrahim Azouani ◽  
Mohamed Amdi
Keyword(s):  
Shape Parameter ◽  
Kernel Method ◽  
Continuation Method ◽  
Path Following ◽  
High Order ◽  
Homotopy Continuation ◽  
Homotopy Continuation Method ◽  
Optimal Value ◽  
Rbf Kernel ◽  
Order Algorithm

AbstractThe goal of this work is to develop a numerical method combining Radial Basic Functions (RBF) kernel and a high order algorithm based on Taylor series and homotopy continuation method. The local RBF approximation applied in strong form allows us to overcome the difficulties of numerical integration and to treat problems of large deformations. Furthermore, the high order algorithm enables to transform the nonlinear problem to a set of linear problems. Determining the optimal value of the shape parameter in RBF kernel is still an outstanding research topic. This optimal value depends on density and distribution of points and the considered problem for e.g. boundary value problems, integral equations, delay-differential equations etc. These have been extensively attempts in literature which end up choosing this optimal value by tests and error or some other ad-hoc means. Our contribution in this paper is to suggest a new strategy using radial basis functions kernel with an automatic reasonable choice of the shape parameter in the nonlinear case which depends on the accuracy and stability of the results. The computational experiments tested on some examples in structural analysis are performed and the comparison with respect to the state of art algorithms from the literature is given.

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