COMPLEXITY OF BEZOUT'S THEOREM IV: PROBABILITY OF SUCCESS; EXTENSIONS
Copyright policy )COMPLEXITY OF BEZOUT'S THEOREM IV: PROBABILITY OF SUCCESS; EXTENSIONS
Summary: We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of \(n\) homogeneous polynomial equations in \(n+ 1\) complex variables of fixed degrees will find all the roots of the system. We also extend the framework of our analysis to cover the classical implicit function theorem and revisit the condition number in this context. Further complexity theory is developed.
- City University of Hong Kong China (People's Republic of)
- IBM (United States) United States
path following, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, projective Newton method, system of polynomial equations, General theory of numerical methods in complex analysis (potential theory, etc.), Complexity and performance of numerical algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), unitary group, Computational aspects of field theory and polynomials, complexity, homotopy methods, Bezout's theorem, integral geometry, condition number
path following, Numerical computation of solutions to systems of equations, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, projective Newton method, system of polynomial equations, General theory of numerical methods in complex analysis (potential theory, etc.), Complexity and performance of numerical algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), unitary group, Computational aspects of field theory and polynomials, complexity, homotopy methods, Bezout's theorem, integral geometry, condition number
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