- Referenced in 204 articles
- Homotopy analysis method in nonlinear differential equations. ”Homotopy Analysis Method in Nonlinear Differential Equations” presents ... highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods...
- Referenced in 236 articles
- wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute...
- Referenced in 81 articles
- solving polynomial systems by the polyhedral homotopy continuation method. HOM4PS-2.0 is a software package ... FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It updates ... method for finding mixed cells; (2) combining the polyhedral and linear homotopies in one step...
- Referenced in 25 articles
- Computing tensor eigenvalues via homotopy methods. We introduce the concept of mode-k generalized eigenvalues ... homotopy continuation type algorithms to solve tensor eigenproblems. With proper implementation, these methods can find ... heuristic approach and a Newton homotopy method to extract real generalized eigenpairs from the found...
- Referenced in 30 articles
- PHoM -- a polyhedral homotopy continuation method for polynomial systems. PHoM is a software package ... polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package ... StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory ... CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions...
- Referenced in 29 articles
- solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes...
- Referenced in 11 articles
- fields of mathematics, science, and engineering. Homotopy continuation methods has been proved ... efficient and reliable class of numerical methods for solving these systems. Hom4PS ... equations that implements many different numerical homotopy methods including the Polyhedral Homotopy continuation method. Based...
- Referenced in 9 articles
- equations Globally convergent, probability-one homotopy methods have proven to be very effective for finding ... equations. After many years of development, homotopy ... path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances ... singular solutions have made probability-one homotopy methods even more practical. POLSYS_GLP consists...
- Referenced in 21 articles
- polynomial system by polyhedral homotopy continuation method. A notable feature of DEMiCs...
- Referenced in 18 articles
- evolution of both theory and codes. Homotopy (continuation) methods are a principal tool for such ... middle game of following a homotopy path is well understood at this point. The paper...
- Referenced in 10 articles
- systems via homotopy continuation and monodromy. This package provides randomized numerical methods for finding complex ... systems of polynomial equations. The main methods implemented in this package find solutions to polynomial ... described in ”Solving polynomial systems via homotopy ... continuation and monodromy” (2016), these methods pair numerical homotopy continuation with the transitive monodromy action...
- Referenced in 7 articles
- improved spectral homotopy analysis method for solving boundary layer problems This article presents an improved ... spectral-homotopy analysis method (ISHAM) for solving nonlinear differential equations. The implementation of this...
- Referenced in 5 articles
- PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems. The polyhedral homotopy ... polynomial equations. PHoM, an implementation of the method in C++, finds all isolated solutions ... constructing a family of modified polyhedral homotopy functions, tracing the solution curves of the homotopy ... size. Many characteristics of the polyhedral homotopy continuation method make parallel implementation efficient and provide...
- Referenced in 14 articles
- Algebraic Geometry for Macaulay2), implements methods of polynomial homotopy continuation to solve systems of polynomial...
- Referenced in 4 articles
- HOPE: A homotopy optimization method for protein structure prediction. We use a homotopy optimization method ... energy associated with a protein model. The method uses the minimum energy conformation ... path of conformations determined by a homotopy between the potential energy functions ... compared to a variant of Newton’s method and to simulated annealing...
- Referenced in 4 articles
- forests and using a fast iterative homotopy method for solving the non-convex optimization problem...
- Referenced in 3 articles
- special homotopy continuation method for a class of polynomial systems. A special homotopy continuation method ... polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions ... systems. The root number bound of this method is between the total degree bound ... efficiency compared to the polyhedral or other homotopies on such systems. As an application...
- Referenced in 3 articles
- through the use of an inexact Newton method. While a diverse set of test cases ... JFNK and the use of homotopy methods...
- Referenced in 23 articles
- varieties. It is based on numerical polynomial homotopy continuation, which is an alternative ... purpose is to interlink the existing symbolic methods of Macaulay2 and the powerful engine ... package exhibit performance competitive with the other homotopy continuation software...
- Referenced in 2 articles
- Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems ... nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly...