Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
The cheater's homotopy: an efficient procedure for solving systems of polynomial equations
SIAM Journal on Numerical Analysis
How we proved that there are exactly 924 cyclic 7-roots
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Factoring rational polynomials over the complex numbers
SIAM Journal on Computing
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Complexity and real computation
Complexity and real computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
MPI-The Complete Reference, Volume 1: The MPI Core
MPI-The Complete Reference, Volume 1: The MPI Core
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algorithms for Quad-Double Precision Floating Point Arithmetic
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Superlinear Performance in Real-Time Parallel Computation
The Journal of Supercomputing
Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers (2nd Edition)
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
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
Computing dynamic output feedback laws with pieri homotopies on a parallel computer
Computing dynamic output feedback laws with pieri homotopies on a parallel computer
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)
Approximate bivariate factorization: a geometric viewpoint
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Adaptive Multiprecision Path Tracking
SIAM Journal on Numerical Analysis
Parallel implementation of polyhedral homotopy methods
Parallel implementation of polyhedral homotopy methods
Concurrent and Real-Time Programming in Ada
Concurrent and Real-Time Programming in Ada
Parallel Implementation of a Subsystem-by-Subsystem Solver
HPCS '08 Proceedings of the 2008 22nd International Symposium on High Performance Computing Systems and Applications
HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems
Parallel Computing
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems
Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems
GNAT pro for on-board mission-critical space applications
Ada-Europe'05 Proceedings of the 10th Ada-Europe international conference on Reliable Software Technologies
Parallel homotopy algorithms to solve polynomial systems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
An automatic parallelization framework for algebraic computation systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Sampling algebraic sets in local intrinsic coordinates
Computers & Mathematics with Applications
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Homotopy continuation methods to solve polynomial systems scale very well on parallel machines. We examine its parallel implementation on multiprocessor multicore workstations using threads. With more cores we speed up pleasingly parallel path tracking jobs. In addition, we compute solutions more accurately in about the same amount of time with threads, and thus achieve quality up. Focusing on polynomial evaluation and linear system solving (key ingredients of Newton's method) we can double the accuracy of the results with the quad doubles of QD-2.3.9 in less than double the time, if all available eight cores are used.