2 research outputs found
A Blackbox Polynomial System Solver on Parallel Shared Memory Computers
A numerical irreducible decomposition for a polynomial system provides
representations for the irreducible factors of all positive dimensional
solution sets of the system, separated from its isolated solutions. Homotopy
continuation methods are applied to compute a numerical irreducible
decomposition. Load balancing and pipelining are techniques in a parallel
implementation on a computer with multicore processors. The application of the
parallel algorithms is illustrated on solving the cyclic -roots problems, in
particular for , and~12.Comment: Accepted for publication in the proceedings of CASC 201
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
We consider the problem of tracking one solution path defined by a polynomial
homotopy on a parallel shared memory computer. Our robust path tracker applies
Newton's method on power series to locate the closest singular parameter value.
On top of that, it computes singular values of the Hessians of the polynomials
in the homotopy to estimate the distance to the nearest different path.
Together, these estimates are used to compute an appropriate adaptive stepsize.
For n-dimensional problems, the cost overhead of our robust path tracker is
O(n), compared to the commonly used predictor-corrector methods. This cost
overhead can be reduced by a multithreaded program on a parallel shared memory
computer.Comment: Accepted for publication in the proceedings of CASC 2020 (Computer
Algebra in Scientific Computing