A search for an optimal start system for numerical homotopy continuation
نویسنده
چکیده
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start systems is a hard problem, our experiments show that it is possible to find start systems that deliver better average complexity than the ones that are commonly used in the existing homotopy continuation software.
منابع مشابه
Polynomial Homotopies for Dense, Sparse and Determinantal Systems
Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution of a generic system that is used to start up the deformations. Software and applications are discussed. AMS Subject Classification. 14N10, 14M15, 52A39, 52B...
متن کاملComputing the optimal partition of variables in multi-homogeneous homotopy methods
The multi-homogenous homotopy continuation method is one of the most efficient approaches in finding all isolated solutions of polynomial systems. A different partition of variables leads to a different homotopy system. The homotopy using the optimal partition of variables reduces the computational cost in curve following to the minimum. However, finding the optimal variable partition is likely...
متن کاملOptimization problem in multi-homogeneous homotopy method
Multi-homogeneous homotopy continuation method is one of the most efficient approaches in solving all isolated solutions of a polynomial system of equations. Finding the optimal partition of variables with the minimal multihomogeneous Bézout number is clearly an optimization problem. Multi-homogeneous continuation using the optimal partition of variables reduces the computational cost in path t...
متن کاملHomotopies for Solving Polynomial Systems Within a Bounded Domain
The problem considered in this paper is the computation of all solutions of a given polynomial system in a bounded domain. Proving Rouché’s Theorem by homotopy continuation concepts yields a new class of homotopy methods, the socalled regional homotopy methods. These methods rely on isolating a part of the system to be solved, which dominates the rest of the system on the border of the domain. ...
متن کاملPHCpack in Macaulay2
The Macaulay2 package PHCpack provides an interface to PHCpack, a generalpurpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The package also provides a fast mixed volume computation, the ability to filter solutions, homotopy path tracking, and a numerical irreducible decomposition method....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1105.4324 شماره
صفحات -
تاریخ انتشار 2011