Treffer: COMPLEXITY OF BEZOUT'S THEOREM IV: PROBABILITY OF SUCCESS; EXTENSIONS: Complexity of Bezout's theorem. IV: Probability of success; extensions

Title:
COMPLEXITY OF BEZOUT'S THEOREM IV: PROBABILITY OF SUCCESS; EXTENSIONS: Complexity of Bezout's theorem. IV: Probability of success; extensions
Authors:
Michael Shub, Steve Smale
Source:
SIAM Journal on Numerical Analysis. 33:128-148
Publisher Information:
World Scientific Publishing Company, 1996.
Publication Year:
1996
Subject Terms:
path following, 4. Education, Numerical computation of solutions to systems of equations, 16. Peace & justice, 01 natural sciences, 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, 0101 mathematics, complexity, homotopy methods, Bezout's theorem, integral geometry, condition number
Document Type:
Buch Part of book or chapter of book<br />Article
File Description:
application/xml
ISSN:
1095-7170
0036-1429
DOI:
10.1142/9789812792839_0019
DOI:
10.1137/0733008
Access URL:
https://epubs.siam.org/doi/abs/10.1137/0733008
Accession Number:
edsair.doi.dedup.....b3cc032b450d13756a2f5fc3bcf55f1a
Database:
OpenAIRE

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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.