Algorithm 835: MultRoot - -a Matlab package for computing polynomial roots and multiplicities MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison.

References in zbMATH (referenced in 82 articles , 1 standard article )

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  1. Bourne, Martin; Winkler, Joab R.; Yi, Su: The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials (2017)
  2. Frauendiener, Jörg; Klein, Christian: Computational approach to compact Riemann surfaces (2017)
  3. Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the distance of coprime polynomials to common divisibility (2017)
  4. Wu, Wenyuan; Zeng, Zhonggang: The numerical factorization of polynomials (2017)
  5. Lee, Hwangrae; Sturmfels, Bernd: Duality of multiple root loci (2016)
  6. Schost, Éric; Spaenlehauer, Pierre-Jean: A quadratically convergent algorithm for structured low-rank approximation (2016)
  7. Winkler, Joab R.: Polynomial computations for blind image deconvolution (2016)
  8. Frauendiener, Jörg; Klein, Christian: Computational approach to hyperelliptic Riemann surfaces (2015)
  9. Hu, Wenyu; Luo, Xingjun; Luo, Zhongxuan: A unified approach to computing the nearest complex polynomial with a given zero (2015)
  10. Ruatta, Olivier; Sciabica, Mark; Szanto, Agnes: Overdetermined Weierstrass iteration and the nearest consistent system (2015)
  11. Shen, Li-Yong; Pérez-Díaz, Sonia: Numerical proper reparametrization of parametric plane curves (2015)
  12. Christou, D.; Karcanias, N.; Mitrouli, M.: Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials (2014)
  13. Li, Zhe; Liu, Qi: A heuristic verification of the degree of the approximate GCD of two univariate polynomials (2014)
  14. Luo, Zhongxuan; Feng, Erbao; Zhang, Jiejin: A numerical realization of the conditions of Max Nöther’s residual intersection theorem (2014)
  15. Winkler, Joab R.: Structured matrix methods for the computation of multiple roots of a polynomial (2014)
  16. Belhaj, Skander: Computing the polynomial remainder sequence via Bézout matrices (2013)
  17. Corless, Robert M.: Pseudospectra of exponential matrix polynomials (2013)
  18. Corless, Robert M.; Fillion, Nicolas: A graduate introduction to numerical methods. From the viewpoint of backward error analysis (2013)
  19. Hodorog, Mădălina; Schicho, Josef: A regularization approach for estimating the type of a plane curve singularity (2013)
  20. Lichtblau, Daniel: Approximate Gröbner bases, overdetermined polynomial systems, and approximate GCDs (2013)

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