2015/05/03 by Jan Verschelde, Verschelde, Jan, Xiangcheng Yu +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1505.00383
openalex publication_date 2015/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy. The data parallelism that provides the speedups stems from the evaluation and differentiation of the monomials in the same polynomial system at different data points, which are the points on the solution paths. Polynomial homotopies that have tens of thousands of solution paths can keep a sufficiently large amount of threads occupied. Our accelerated code combines the reverse mode of algorithmic differentiation with double double and quad double precision to compute more accurate results faster.