- Referenced in 185 articles
- wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute...
- Referenced in 66 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 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...
- Referenced in 27 articles
- solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes...
- Referenced in 21 articles
- polynomial system by polyhedral homotopy continuation method. A notable feature of DEMiCs...
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- 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...
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- fields of mathematics, science, and engineering. Homotopy continuation methods has been proved ... numerical homotopy methods including the Polyhedral Homotopy continuation method. Based on the successful software package...
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- PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems The polyhedral homotopy ... continuation method (PHoM) is known to be a successful method for finding all isolated solutions ... modified polyhedral homotopy functions, tracing the solution curves of the homotopy equations, and verifying ... size. Many characteristics of the polyhedral homotopy continuation method make parallel implementation efficient and provide...
- Referenced in 13 articles
- Algebraic Geometry for Macaulay2), implements methods of polynomial homotopy continuation to solve systems of polynomial...
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- special homotopy continuation method for a class of polynomial systems. A special homotopy continuation method...
- Referenced in 16 articles
- based on numerical polynomial homotopy continuation, which is an alternative to the classical symbolic approaches ... purpose is to interlink the existing symbolic methods of Macaulay2 and the powerful engine ... exhibit performance competitive with the other homotopy continuation software...
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- 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 11 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 ... combines a heuristic approach and a Newton homotopy method to extract real generalized eigenpairs from...
- Referenced in 46 articles
- first stage a first-order iterative “shrinkage” method yields an estimate of the subset ... basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence...
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- polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver ... volume computation, the ability to filter solutions, homotopy path tracking, and a numerical irreducible decomposition...
- Referenced in 5 articles
- primal SVM. Then the optimal gradient method without any line search is adopted to solve ... homotopy NESVM” to accelerate NESVM by dynamically decreasing the smooth parameter and using the continuation ... method. Our experiments on census income categorization, indoor/outdoor scene classification event recognition and scene recognition...
- Referenced in 17 articles
- theorem proving, by situating automated tools and methods in a framework that supports user interaction ... currently being used to formalize category theory, homotopy type theory, and abstract algebra. We describe ... main features, and we discuss applications and continuing work...
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- through the use of an inexact Newton method. While a diverse set of test cases ... does the Picard solver). Globalization through parameter continuation did not remedy this problem and future ... JFNK and the use of homotopy methods...
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- package relies on methods of numerical algebraic geometry, such as homotopy continuation and monodromy...
- Referenced in 47 articles
- ACRITH-XSC is a Fortran-like programming language...