Numerical Solution of a Class of Deficient Polynomial Systems
- 1 April 1987
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 24 (2) , 435-451
- https://doi.org/10.1137/0724032
Abstract
Most systems of polynomials which arise in applications have fewer than the expected number of solutions. The amount of computation required to find all solutions of such a “deficient” system using current homotopy continuation methods is proportional to the expected number of solutions and, roughly, to the size of the system. Much time is wasted following paths which do not lead to solutions. We suggest methods for solving some deficient polynomial systems for which the amount of computational effort is instead proportional to the number of solutions.Keywords
This publication has 13 references indexed in Scilit:
- Regularity results for solving systems of polynomials by homotopy methodNumerische Mathematik, 1986
- A homotopy for solving polynomial systemsApplied Mathematics and Computation, 1986
- Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation MethodsJournal of Mechanical Design, 1985
- Intersection TheoryPublished by Springer Nature ,1984
- On the Number of Solutions to Polynomial Systems of EquationsSIAM Journal on Numerical Analysis, 1980
- Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of EquationsSIAM Review, 1980
- Determining All Solutions to Certain Systems of Nonlinear EquationsMathematics of Operations Research, 1979
- A homotopy method for locating all zeros of a system of polynomialsLecture Notes in Mathematics, 1979
- Eine Methode zur berechnung s mtlicher L sungen von PolynomgleichungssystemenNumerische Mathematik, 1977
- Algebraic GeometryPublished by Springer Nature ,1977