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JUCS
2010
106views more  JUCS 2010»
13 years 6 months ago
A Heuristic Approach to Positive Root Isolation for Multiple Power Sums
: Given a multiple power sum (extending polynomial’s exponents to real numbers), the positive root isolation problem is to find a list of disjoint intervals, satisfying that the...
Ming Xu, Chuandong Mu, Zhenbing Zeng, Zhi-bin Li
CORR
2007
Springer
96views Education» more  CORR 2007»
13 years 8 months ago
New Complexity Bounds for Certain Real Fewnomial Zero Sets
d Abstract) Frederic Bihan∗ Joel Gomez† Andrew Niles‡ J. Maurice Rojas§ January 24, 2007 Rojas dedicates this paper to his friend, Professor Tien-Yien Li. Consider real biv...
Joel Gomez, Andrew Niles, J. Maurice Rojas
CORR
2010
Springer
138views Education» more  CORR 2010»
13 years 8 months ago
Shallow Circuits with High-Powered Inputs
A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show ...
Pascal Koiran
CASC
2009
Springer
157views Mathematics» more  CASC 2009»
14 years 3 months ago
On the Complexity of Reliable Root Approximation
This work addresses the problem of computing a certified ǫ-approximation of all real roots of a square-free integer polynomial. We proof an upper bound for its bit complexity, b...
Michael Kerber
ISSAC
2009
Springer
121views Mathematics» more  ISSAC 2009»
14 years 3 months ago
Faster real feasibility via circuit discriminants
We show that detecting real roots for honestly n-variate (n + 2)-nomials (with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any ...
Frédéric Bihan, J. Maurice Rojas, Ca...