Heuristic quadratic approximation for the universality theorem. Salinas, L. C., Plaza, R., & Hernández, G. Cluster Computing, 17(2):281-289, 2014.
Voronin's Universality Theorem states grosso modo, that any non-vanishing analytic function can be uniformly approximated by certain shifts of the Riemann zeta-function ζ(s). However, the problem of obtaining a concrete approximants for a given function is computationally highly challenging. The present note deals with this problem, using a finite number n of factors taken from the Euler product definition of ζ(s). The main result of the present work is the design and implementation of a sequential and a parallel heuristic method for the computation of those approximants. The main properties of this method are: (i) the computation time grows quadratically as a function of the quotient n/m, where m is the number of coefficients calculated in one iteration of the heuristic; (ii) the error does not vary significantly as m changes and is similar to the error of the exact algorithm. © 2013 Springer Science+Business Media New York.
@article{10.1007/s10586-013-0312-5,
abstract = "Voronin's Universality Theorem states grosso modo, that any non-vanishing analytic function can be uniformly approximated by certain shifts of the Riemann zeta-function ζ(s). However, the problem of obtaining a concrete approximants for a given function is computationally highly challenging. The present note deals with this problem, using a finite number n of factors taken from the Euler product definition of ζ(s). The main result of the present work is the design and implementation of a sequential and a parallel heuristic method for the computation of those approximants. The main properties of this method are: (i) the computation time grows quadratically as a function of the quotient n/m, where m is the number of coefficients calculated in one iteration of the heuristic; (ii) the error does not vary significantly as m changes and is similar to the error of the exact algorithm. © 2013 Springer Science+Business Media New York.",
number = "2",
year = "2014",
title = "Heuristic quadratic approximation for the universality theorem",
volume = "17",
keywords = "Heuristic , Quadratic , Universality theorem",
pages = "281-289",
doi = "10.1007/s10586-013-0312-5",
journal = "Cluster Computing",
author = "Salinas, Luís C. and Plaza, Rafael and Hernández, Gonzalo"
}