Complexity of Bezout's Theorem IV: Probability of Success; Extensions
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 class...
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| Veröffentlicht in: | SIAM journal on numerical analysis 1996-02, Vol.33 (1), p.128-148 |
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| container_end_page | 148 |
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| container_title | SIAM journal on numerical analysis |
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| creator | Shub, Michael Smale, Steve |
| description | 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. |
| doi_str_mv | 10.1137/0733008 |
| format | Article |
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| ispartof | SIAM journal on numerical analysis, 1996-02, Vol.33 (1), p.128-148 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; JSTOR |
| subjects | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximate zero Complexity theory Computer science control theory systems Differential geometry Economic theory Exact sciences and technology Geometry Great circles Mathematical constants Mathematical theorems Mathematics Newtons method Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Polynomials Riemann manifold Sciences and techniques of general use Success Theoretical computing Zero |
| title | Complexity of Bezout's Theorem IV: Probability of Success; Extensions |
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