MPSolve

Polynomial Computations The research in this field concerns the design and analysis of algorithms for solving problems involving polynomial computations. The interplay between structured matrices and polynomial computations plays an important role in our analysis. The main problems investigated are related to the solution of (systems of) polynomial equations, polynomial arithmetic, gcd and lcm computations, Euclidean algorithm, polynomial and power series factorizations, spectral factorizations, matrix polynomials and matrix power series, interpolation problems, orthogonal polynomials and rational functions.Efficiency of the algorithms in terms of their complexity and stability is pursued. (Source: http://plato.asu.edu)


References in zbMATH (referenced in 13 articles )

Showing results 1 to 13 of 13.
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  1. Bini, Dario A.; Robol, Leonardo: Solving secular and polynomial equations: a multiprecision algorithm (2014)
  2. Jacobsen, Jesper Lykke; Salas, Jesús: A generalized Beraha conjecture for non-planar graphs (2013)
  3. Kamath, Narayan; Voiculescu, Irina; Yap, Chee K.: Empirical study of an evaluation-based subdivision algorithm for complex root isolation (2011)
  4. Pan, Victor Y.; Zheng, Ai-Long: New progress in real and complex polynomial root-finding (2011)
  5. Salas, Jesús; Sokal, Alan D.: Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial (2009)
  6. Chen, Danny Z.; Daescu, Ovidiu; Dai, Yang; Katoh, Naoki; Wu, Xiaodong; Xu, Jinhui: Efficient algorithms and implementations for optimizing the sum of linear fractional functions, with applications (2005)
  7. Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.: Spanning forests and the $q$-state Potts model in the limit $q \to 0$ (2005)
  8. Revol, Nathalie; Rouillier, Fabrice: Motivations for an arbitrary precision interval arithmetic and the MPFI library (2005)
  9. Traczinski, Daniela; Luther, Wolfram; Haßlinger, Gerhard: Polynomial factorization for servers with semi-Markovian workload: Performance and numerical aspects of a verified solution technique (2005)
  10. Fausten, Daniela; Luther, Wolfram; Haßlinger, Gerhard: Accurate computation of traffic workload distributions (2004)
  11. Rouillier, Fabrice; Zimmermann, Paul: Efficient isolation of polynomial’s real roots. (2004)
  12. Royle, Gordon; Sokal, Alan D.: The Brown-Colbourn conjecture on zeros of reliability polynomials is false (2004)
  13. Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.: Transfer matrices and partition-function zeros for antiferromagnetic Potts models. III: Triangular-lattice chromatic polynomial (2003)