Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems
نویسندگان
چکیده
منابع مشابه
Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems
How many operations do we need on the average to compute an approximate root of a random Gaussian polynomial system? Beyond Smale’s 17th problem that asked whether a polynomial bound is possible, we prove a quasi-optimal bound (input size)1`op1q. This improves upon the previously known (input size) 3 2 `op1q bound. The new algorithm relies on numerical continuation along rigid continuation path...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2019
ISSN: 0894-0347,1088-6834
DOI: 10.1090/jams/938