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FOCM
2008
76views more  FOCM 2008»
13 years 8 months ago
On Smale's 17th Problem: A Probabilistic Positive Solution
Smale's 17th Problem asks "Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the s...
Carlos Beltrán, Luis Miguel Pardo
CORR
2008
Springer
131views Education» more  CORR 2008»
13 years 8 months ago
Optimizing polynomials for floating-point implementation
The floating-point implementation of a function often reduces to a polynomial approximation on an interval. Remez algorithm provides the polynomial closest to the function, but th...
Florent de Dinechin, Christoph Quirin Lauter
TOC
2010
155views Management» more  TOC 2010»
13 years 3 months ago
A New Quantum Lower Bound Method, with an Application to a Strong Direct Product Theorem for Quantum Search
Abstract: We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structur...
Andris Ambainis
ISSAC
2007
Springer
93views Mathematics» more  ISSAC 2007»
14 years 2 months ago
Approximate bivariate factorization: a geometric viewpoint
We briefly present and analyze, from a geometric viewpoint, strategies for designing algorithms to factor bivariate approximate polynomials in   [x, y]. Given a composite polyno...
André Galligo, Mark van Hoeij
COCO
2004
Springer
185views Algorithms» more  COCO 2004»
14 years 9 days ago
Limitations of Quantum Advice and One-Way Communication
Abstract: Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accesse...
Scott Aaronson