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MICS
2007
128views more  MICS 2007»
9 years 1 months ago
Structured Low Rank Approximation of a Bezout Matrix
The task of determining the approximate greatest common divisor (GCD) of more than two univariate polynomials with inexact coefficients can be formulated as computing for a given B...
Dongxia Sun, Lihong Zhi
JSC
2006
76views more  JSC 2006»
9 years 2 months ago
Fast computation of special resultants
We propose fast algorithms for computing composed products and composed sums, as well as diamond products of univariate polynomials. These operations correspond to special multiva...
Alin Bostan, Philippe Flajolet, Bruno Salvy, &Eacu...
CAGD
2008
80views more  CAGD 2008»
9 years 2 months ago
Division algorithms for Bernstein polynomials
Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for c...
Laurent Busé, Ron Goldman
STOC
1995
ACM
135views Algorithms» more  STOC 1995»
9 years 5 months ago
Subquadratic-time factoring of polynomials over finite fields
New probabilistic algorithms are presented for factoring univariate polynomials over finite fields. The algorithms factor a polynomial of
Erich Kaltofen, Victor Shoup
COMPGEOM
2001
ACM
9 years 6 months ago
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
We present two approaches to the problem of calculating a cell in a 3-dimensional arrangement of quadrics. The first approach solves the problem using rational arithmetic. It work...
Nicola Geismann, Michael Hemmer, Elmar Schöme...
COLT
2000
Springer
9 years 6 months ago
Average-Case Complexity of Learning Polynomials
The present paper deals with the averagecase complexity of various algorithms for learning univariate polynomials. For this purpose an appropriate framework is introduced. Based o...
Frank Stephan, Thomas Zeugmann
CASC
2005
Springer
202views Mathematics» more  CASC 2005»
9 years 7 months ago
Cayley-Dixon Resultant Matrices of Multi-univariate Composed Polynomials
The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in w...
Arthur D. Chtcherba, Deepak Kapur, Manfred Minimai...
ACL2
2006
ACM
9 years 8 months ago
Unique factorization in ACL2: Euclidean domains
ACL2 is used to systematically study domains whose elements can be “uniquely” factored into products of “irreducible” elements. The best known examples of such domains are...
John R. Cowles, Ruben Gamboa
FOCS
2008
IEEE
9 years 8 months ago
Fast Modular Composition in any Characteristic
We give an algorithm for modular composition of degree n univariate polynomials over a finite field Fq requiring n1+o(1) log1+o(1) q bit operations; this had earlier been achiev...
Kiran S. Kedlaya, Christopher Umans
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