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CORR
2011
Springer
155views Education» more  CORR 2011»
7 years 7 months ago
On the Generation of Positivstellensatz Witnesses in Degenerate Cases
One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomi...
David Monniaux, Pierre Corbineau
SIAMNUM
2010
87views more  SIAMNUM 2010»
7 years 10 months ago
A Note on the Computation of All Zeros of Simple Quaternionic Polynomials
Polynomials with quaternionic coefficients located on only one side of the powers (we call them simple polynomials) may have two different types of zeros: isolated and spherical ze...
Drahoslava Janovská, Gerhard Opfer
SIAMJO
2010
107views more  SIAMJO 2010»
7 years 10 months ago
Error Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube
We consider the problem of minimizing a polynomial on the hypercube [0, 1]n and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem...
Etienne de Klerk, Monique Laurent
JOC
2010
96views more  JOC 2010»
7 years 10 months ago
On the Efficient Generation of Prime-Order Elliptic Curves
We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the ...
Elisavet Konstantinou, Aristides Kontogeorgis, Yan...
IJNSEC
2010
324views more  IJNSEC 2010»
7 years 10 months ago
Computing the Modular Inverse of a Polynomial Function over GF(2P) Using Bit Wise Operation
Most public key crypto systems use finite field modulo arithmetic. This modulo arithmetic is applied on real numbers, binary values and polynomial functions. The computation cost ...
Rajaram Ramasamy, Amutha Prabakar Muniyandi
SIAMSC
2011
177views more  SIAMSC 2011»
7 years 10 months ago
Computing f(A)b via Least Squares Polynomial Approximations
Given a certain function f, various methods have been proposed in the past for addressing the important problem of computing the matrix-vector product f(A)b without explicitly comp...
Jie Chen, Mihai Anitescu, Yousef Saad
MOC
2011
7 years 10 months ago
Regeneration homotopies for solving systems of polynomials
We present a new technique, based on polynomial continuation, for solving systems of n polynomials in N complex variables. The method allows equations to be introduced one-by-one o...
Jonathan D. Hauenstein, Andrew J. Sommese, Charles...
JAT
2011
81views more  JAT 2011»
7 years 10 months ago
Polynomial reproduction for univariate subdivision schemes of any arity
In this paper we study the ability of convergent subdivision schemes to reproduce polynomials in the sense that for initial data, which is sampled from some polynomial function, t...
Costanza Conti, Kai Hormann
ECCC
2011
223views ECommerce» more  ECCC 2011»
7 years 10 months ago
A Case of Depth-3 Identity Testing, Sparse Factorization and Duality
Polynomial identity testing (PIT) problem is known to be challenging even for constant depth arithmetic circuits. In this work, we study the complexity of two special but natural ...
Chandan Saha, Ramprasad Saptharishi, Nitin Saxena
CORR
2011
Springer
146views Education» more  CORR 2011»
7 years 10 months ago
Refined bounds on the number of connected components of sign conditions on a variety
Let R be a real closed field, P, Q ⊂ R[X1, . . . , Xk] finite subsets of polynomials, with the degrees of the polynomials in P (resp. Q) bounded by d (resp. d0). Let V ⊂ Rk b...
Sal Barone, Saugata Basu
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