CORR
2011
Springer
12 years 8 months ago
2011
Springer
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...
SIAMNUM
2010
12 years 11 months ago
2010
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...
SIAMJO
2010
12 years 11 months ago
2010
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...
JOC
2010
12 years 11 months ago
2010
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 ...
IJNSEC
2010
12 years 11 months ago
2010
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 ...
SIAMSC
2011
12 years 11 months ago
2011
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...
MOC
2011
12 years 11 months ago
2011
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...
JAT
2011
12 years 11 months ago
2011
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...
ECCC
2011
12 years 11 months ago
2011
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 ...
CORR
2011
Springer
12 years 11 months ago
2011
Springer
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...