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- Jérôme Brachat, Pierre Comon, Bernard Mourrain, Elias P. Tsigaridas
- 2009 17th European Signal Processing Conference
- 2009

We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric tensors of dimension 2. We exploit the known fact that every symmetric tensor is equivalently represented by a homogeneous polynomial in n variables of total degree… (More)

- Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsigaridas
- Reliable Implementation of Real Number Algorithms
- 2008

We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree d, with integer coefficients of bit size ≤ τ , using Sturm (-Habicht) sequences and the Bernstein subdivision solver. In particular, we unify and simplify the analysis of both methods and we give an asymptotic complexity bound of e OB(d τ).… (More)

- Jin-San Cheng, Sylvain Lazard, Luis Mariano Peñaranda, Marc Pouget, Fabrice Rouillier, Elias P. Tsigaridas
- Mathematics in Computer Science
- 2010

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic… (More)

In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be described equivalently in the spherical harmonic (SH) basis, in the symmetric tensor (ST) basis constrained to the sphere, and in the homogeneous polynomial (HP) basis constrained to the sphere. All three bases span the same vector… (More)

We present a cgal-based univariate algebraic kernel, which provides certi ed real-root isolation of univariate polynomials with integer coe cients and standard functionalities such as basic arithmetic operations, greatest common divisor (gcd) and square-free factorization, as well as comparison and sign evaluations of real algebraic numbers. We compare our… (More)

- Victor Y. Pan, Elias P. Tsigaridas
- SNC
- 2000

We estimate the Boolean complexity of multiplication of structured matrices by a vector and the solution of nonsingular linear systems of equations with these matrices. We study four basic and most popular classes, that is, Toeplitz, Hankel, Cauchy and Vandermonde matrices, for which the cited computational problems are equivalent to the task of polynomial… (More)

- Dimitrios I. Diochnos, Ioannis Z. Emiris, Elias P. Tsigaridas
- J. Symb. Comput.
- 2009

This paper is concerned with exact real solving of well-constrained, bivariate polynomial systems. The main problem is to isolate all common real roots in rational rectangles, and to determine their intersection multiplicities. We present three algorithms and analyze their asymptotic bit complexity, obtaining a bound of ÕB(N ) for the purely… (More)

We consider exact real solving of well-constrained, bivariate systems of relatively prime polynomials. The main problem is to compute all common real roots in isolating interval representation, and to determine their intersection multiplicities. We present three algorithms and analyze their asymptotic bit complexity, obtaining a bound of… (More)

- Ioannis Z. Emiris, Elias P. Tsigaridas, George M. Tzoumas
- Symposium on Computational Geometry
- 2006

This paper examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete algorithms, under the exact computation paradigm, for the predicates of an incremental algorithm: κ<sub>1</sub> decides which one of 2 given ellipses is closest to a given exterior point; κ<sub>2</sub> decides the… (More)

- Milan Hladík, David Daney, Elias P. Tsigaridas
- SIAM J. Matrix Analysis Applications
- 2010

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on one hand such interval matrices have many applications in mechanics and engineering, and on the other many… (More)