Some examples for solving systems of algebraic equations by calculating groebner bases
Journal of Symbolic Computation
A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
A globally convergent parallel algorithm for zeros of polynomial systems
Non-Linear Analysis
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Control and Optimization
ACM Transactions on Mathematical Software (TOMS)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Numerical Schubert Calculus by the Pieri Homotopy Algorithm
SIAM Journal on Numerical Analysis
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
SIAM Journal on Numerical Analysis
The Parallel Complexity of Embedding Algorithms for the Solution of Systems of Nonlinear Equations
IEEE Transactions on Parallel and Distributed Systems
The Granularity of Homotopy Algorithms for Polynomial Systems of Equations
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
Computing Feedback Laws for Linear Systems with a Parallel Pieri Homotopy
ICPPW '04 Proceedings of the 2004 International Conference on Parallel Processing Workshops
Factoring Solution Sets of Polynomial Systems in Parallel
ICPPW '05 Proceedings of the 2005 International Conference on Parallel Processing Workshops
Algorithm 846: MixedVol: a software package for mixed-volume computation
ACM Transactions on Mathematical Software (TOMS)
Parallel Implementation of the Polyhedral Homotopy Method
ICPPW '06 Proceedings of the 2006 International Conference Workshops on Parallel Processing
ACM Transactions on Mathematical Software (TOMS)
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Interfacing with the numerical homotopy algorithms in PHCpack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Computing monodromy via parallel homotopy continuation
Proceedings of the 2007 international workshop on Parallel symbolic computation
ACM Communications in Computer Algebra
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Interfacing with the numerical homotopy algorithms in PHCpack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as “embarrassingly parallel”, i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarrassing not to develop parallel implementations of polynomial homotopy continuation methods. This paper concerns the development of “parallel PHCpack”, a project which started a couple of years ago in collaboration with Yusong Wang, and which currently continues with Anton Leykin (parallel irreducible decomposition) and Yan Zhuang (parallel polyhedral homotopies). We report on our efforts to make PHCpack ready to solve large polynomial systems which arise in applications. 2000 Mathematics Subject Classification. Primary 65H10. Secondary 14Q99, 68W30.