Add to ORKGLet p∈Z[x] be an arbitrary polynomial of degree n with k non-zero integer coefficients of absolute value less than 2τ. We show that the real roots of p can be computed with a number of arithmetic operations over the rational numbers that is polynomial in the in-put size of the sparse representation of p. More precisely, we give a deterministic, complete, and certified algorithm that determines isolating intervals for all real roots of p with O(k3 · log(nτ) · logn) many exact arithmetic operations over the rational numbers. When using approximate but certified arithmetic, the bit com-plexity of our algorithm is bounded by1 Õ(k4 · nτ). Hence, for sufficiently sparse polynomials (i.e. k = O(logc(nτ)) for a positive constant c), the bit compl...
AbstractLet f be a degree D univariate polynomial with real coefficients and exactly m monomial term...
We show that deciding whether a sparse polynomial in one variable has a root in Fp (for p prime) is ...
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We descr...
We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x...
We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x...
Given a polynomial p(z) of degree n with integer coefficients, whose absolute values are bounded abo...
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms t...
We consider the problem of approximating all real roots of a square-free polynomial f. Given isolati...
AbstractWe present a simple algorithm for approximating all roots of a polynomial p(x) when it has o...
We consider a univariate polynomial f with real coecients having a high degree N but a rather small ...
The problem of computing the roots of a particular sequence of sparse polynomials pn(t) is considere...
The problem of computing the roots of a particular sequence of sparse polynomials pn(t) is considere...
AbstractLet f be a degree D univariate polynomial with real coefficients and exactly m monomial term...
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We descr...
AbstractGiven a univariate polynomialf(z) of degreenwith complex coefficients, whose norms are less ...
AbstractLet f be a degree D univariate polynomial with real coefficients and exactly m monomial term...
We show that deciding whether a sparse polynomial in one variable has a root in Fp (for p prime) is ...
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We descr...
We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x...
We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x...
Given a polynomial p(z) of degree n with integer coefficients, whose absolute values are bounded abo...
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms t...
We consider the problem of approximating all real roots of a square-free polynomial f. Given isolati...
AbstractWe present a simple algorithm for approximating all roots of a polynomial p(x) when it has o...
We consider a univariate polynomial f with real coecients having a high degree N but a rather small ...
The problem of computing the roots of a particular sequence of sparse polynomials pn(t) is considere...
The problem of computing the roots of a particular sequence of sparse polynomials pn(t) is considere...
AbstractLet f be a degree D univariate polynomial with real coefficients and exactly m monomial term...
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We descr...
AbstractGiven a univariate polynomialf(z) of degreenwith complex coefficients, whose norms are less ...
AbstractLet f be a degree D univariate polynomial with real coefficients and exactly m monomial term...
We show that deciding whether a sparse polynomial in one variable has a root in Fp (for p prime) is ...
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We descr...