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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 4 τ… (More)

- Elias P. Tsigaridas, Ioannis Z. Emiris
- Theor. Comput. Sci.
- 2008

We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method's good performance in practice. We derive an expected complexity bound of O B (d 6 + d 4 τ 2), where d is the polynomial… (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)

Our work goes towards answering the growing need for the robust and efficient manipulation of curved objects in numerous applications. The kernel of the cgal library provides several functionalities which are, however, mostly restricted to linear objects. We focus here on the arrangement of conic arcs in the plane. Our first contribution is the design,… (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 OB(N 14) for the purely… (More)

- Jin-San Cheng, Sylvain Lazard, Luis Mariano Peñaranda, Marc Pouget, Fabrice Rouillier, Elias P. Tsigaridas
- Symposium on Computational Geometry
- 2009

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)

Real solving of univariate polynomials is a fundamental problem with several important applications. This paper is focused on the comparison of black-box implementations of state-of-the-art algorithms for isolating real roots of univariate polynomials over the integers. We have tested 9 different implementations based on symbolic-numeric methods, Sturm… (More)

- Elias P. Tsigaridas, Ioannis Z. Emiris
- ESA
- 2006

We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method's good performance in practice. We improve the previously known bound by a factor of dτ , where d is the polynomial degree and… (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)