Paper Info
Title
Abstract only: Certified numerical solving of systems of polynomial equations
Abstract
Polynomial homotopy continuation is at the heart of numerical algebraic geometry, an area whose primary goal is to solve systems of polynomial equations. Recently this field developed rapidly producing several software packages that solve some problems out of reach for purely symbolic techniques. However, the homotopy tracking procedures employ heuristics to follow the homotopy continuation paths. Jointly with Carlos Beltran we have devised a certified homotopy tracking algorithm, which was implemented in Macaulay2. In addition we conducted experiments shedding light on some developments in complexity analysis of polynomial systems solving.
Year
DOI
Venue
2010
10.1145/1838599.1838610
ACM Comm. Computer Algebra
Keywords
Field
DocType
numerical algebraic geometry,complexity analysis,homotopy continuation path,certified homotopy tracking algorithm,polynomial homotopy continuation,primary goal,carlos beltran,polynomial equation,polynomial system,homotopy tracking procedure
Discrete mathematics,Combinatorics,Algebra,Polynomial,System of polynomial equations,Heuristics,Software,Homotopy continuation,Homotopy,Homotopy analysis method,Certification,Mathematics
Journal
Volume
Issue
Citations 
44
1/2
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Anton Leykin117318.99