Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study
Copyright policy )Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study
A family of systems of polynomial equations is considered, which arises in the analysis of the stationary solutions of certain discretized semi-linear parabolic differential equations. Only the positive solutions are of interest. A numerical homotopy algorithm for finding all positive solutions is presented with polynomial complexity in the number of unknown. It is shown that any universal symbolic method is likely to have a complexity which is exponential in the number of unknowns.
- National Scientific and Technical Research Council Argentina
- Universidid De Buenos Aires Argentina
- National University of General Sarmiento Argentina
- University of Buenos Aires Argentina
- Facultad de Ciencias Agrarias y Forestales Argentina
Statistics and Probability, positive solutions, Control and Optimization, Analysis of algorithms and problem complexity, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Matrix algebra, Polynomials, Polynomial system solving, Boundary value problems, Complexity and performance of numerical algorithms, semi-linear parabolic problems, Homotopy algorithms, symbolic methods, Stationary solutions, Computational aspects of field theory and polynomials, Semi-linear parabolic problems, Mathematical models, Numerical Analysis, Algebra and Number Theory, Applied Mathematics, Complexity, polynomial systems, Partial differential equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Real polynomials: location of zeros, Computational complexity, Semi linear parabolic problems, Set theory, complexity, Algorithms, homotopy methods, Conditioning
Statistics and Probability, positive solutions, Control and Optimization, Analysis of algorithms and problem complexity, Numerical computation of solutions to systems of equations, Symbolic computation and algebraic computation, Matrix algebra, Polynomials, Polynomial system solving, Boundary value problems, Complexity and performance of numerical algorithms, semi-linear parabolic problems, Homotopy algorithms, symbolic methods, Stationary solutions, Computational aspects of field theory and polynomials, Semi-linear parabolic problems, Mathematical models, Numerical Analysis, Algebra and Number Theory, Applied Mathematics, Complexity, polynomial systems, Partial differential equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Real polynomials: location of zeros, Computational complexity, Semi linear parabolic problems, Set theory, complexity, Algorithms, homotopy methods, Conditioning
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