A Deterministic Algorithm to Compute Approximate Roots of Polynomial Systems in Polynomial Average Time

We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum–Shub–Smale model with square root. It rests upon a derandomization of an algorithm of Beltrán and Pa...

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Vydané v:	Foundations of computational mathematics Ročník 17; číslo 5; s. 1265 - 1292
Hlavný autor:	Lairez, Pierre
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.10.2017 Springer Nature B.V Springer Verlag
Predmet:	Algorithms Applications of Mathematics Computational Complexity Computer Science Economics Linear and Multilinear Algebras Math Applications in Computer Science Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Primary 68Q25 Secondary 65H10 65H20 Polynomial system Homotopy continuation 65Y20 Smale’s 17th problem Derandomization Complexity homotopy continuation complexity derandomization Smale's 17th problem
ISSN:	1615-3375, 1615-3383
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