Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking

2011/09/02 by Jan Verschelde, Verschelde, Jan, Genady Yoffe +1 · 1 citation
Computer Science · #Cryptography and Residue Arithmetic #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Parallel #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #and Cluster Computing (cs.DC)

paper · pdf · doi:10.48550/arxiv.1109.0545

openalex publication_date 2011/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we describe our multithreaded implementation to track one solution path defined by a polynomial homotopy. Limiting quality to accuracy and confusing accuracy with precision, we strive to offset the cost of multiprecision arithmetic running multithreaded code on many cores.

Cited by

• Evaluating polynomials in several variables and their derivatives on a\n GPU computing processor

Related

• Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit
• Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double Arithmetic
• Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
• A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy\n Continuation
• Mixed Precision Path Tracking for Polynomial Homotopy Continuation