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Symmetric tensor decomposition
- Jérôme Brachat, P. Comon, B. Mourrain, E. Tsigaridas
- Computer Science, MathematicsEuropean Signal Processing Conference
- 23 January 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…
Experimental evaluation and cross-benchmarking of univariate real solvers
- M. Hemmer, E. Tsigaridas, Z. Zafeirakopoulos, I. Emiris, M. Karavelas, B. Mourrain
- Computer ScienceSNC '09
- 3 August 2009
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 and indicates that for most instances the solvers based on Continued Fractions are among the best methods.
The DMM bound: multivariate (aggregate) separation bounds
- I. Emiris, B. Mourrain, E. Tsigaridas
- Mathematics, Computer ScienceInternational Symposium on Symbolic and Algebraic…
- 31 May 2010
The analysis provides a precise asymptotic upper bound on the number of steps that subdivision-based algorithms perform in order to isolate all real roots of a polynomial system, which leads to the first complexity bound of Milne's algorithm in 2D.
On the Topology of Real Algebraic Plane Curves
- Jin-San Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. Rouillier, E. Tsigaridas
- Computer Science, MathematicsMathematics and Computer Science
- 9 October 2010
This work revisits the problem of computing the topology and geometry of a real algebraic plane curve with a novelty of replacing Gröbner basis computations and isolation with rational univariate representations and induces a new approach for computing an arrangement of polylines isotopic to the input curve.
Real Algebraic Numbers: Complexity Analysis and Experimentations
We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree $d$, with integer coefficients of bit size $\le\tau$, using Sturm (-Habicht)…
A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the Orientation Distribution Function in…
- Aurorata Ghosh, E. Tsigaridas, M. Descoteaux, P. Comon, B. Mourrain, R. Deriche
- 10 September 2008
In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be de- scribed equivalently in the spherical harmonic (SH) basis, in the…
On the asymptotic and practical complexity of solving bivariate systems over the reals
Towards and open curved kernel
- I. Emiris, Athanasios Kakargias, S. Pion, M. Teillaud, E. Tsigaridas
- Computer ScienceSCG '04
- 8 June 2004
This work goes towards answering the growing need for the robust and efficient manipulation of curved objects in numerous applications by design, implementation and testing of a kernel for computing arrangements of circular arcs.
Exact Algorithms for Solving Stochastic Games
- Kristoffer Arnsfelt Hansen, M. Koucký, N. Lauritzen, Peter Bro Miltersen, E. Tsigaridas
- Computer Science, EconomicsArXiv
- 17 February 2012
Algorithms for exactly solving Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastically games, when the number of positions of the game is constant, run in polynomial time.