Fast computation of zeros of polynomial systems with bounded degree under finite-precision

Title: Fast computation of zeros of polynomial systems with bounded degree under finite-precision
Creator: Briquel, Irenee; Cucker, Felipe; Peña, Javier; Roshchina, Vera
Date: 2014
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/43143
Identifier: vital:5778
Identifier: https://doi.org/10.1090/S0025-5718-2013-02765-2
Identifier: ISSN:0025-5718
Abstract: A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite precision. In this paper we describe a finite-precision version of this algorithm. Our main result shows that this version works within the same time bounds and requires a precision which, on the average, amounts to a polynomial amount of bits in the mantissa of the intervening floating-point numbers. © 2013 American Mathematical Society.
Relation: Mathematics of Computation Vol. 83, no. 287 (2014), p. 1279-1317
Rights: Copyright American Mathematical Society
Rights: This metadata is freely available under a CCO license
Subject: 0102 Applied Mathematics; Finite-precision; Polynomial systems; Smale's 17th problem
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