An iterated eigenvalue algorithm for approximating roots of univariate polynomials. The author studies an iterative algorithm that approximates all roots of a univariate polynomial. The iteration is based on floating-point computation of the eigenvalues of a generalized companion matrix. A few interesting examples including ill-conditioned polynomials are carefully implemented for the algorithms.

References in zbMATH (referenced in 19 articles )

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  1. Becker, Ruben; Sagraloff, Michael; Sharma, Vikram; Yap, Chee: A near-optimal subdivision algorithm for complex root isolation based on the Pellet test and Newton iteration (2018)
  2. Pan, Victor Y.; Tsigaridas, Elias: Accelerated approximation of the complex roots and factors of a univariate polynomial (2017)
  3. Pan, Victor Y.; Zhao, Liang: Real polynomial root-finding by means of matrix and polynomial iterations (2017)
  4. Schleicher, Dierk; Stoll, Robin: Newton’s method in practice: finding all roots of polynomials of degree one million efficiently (2017)
  5. Wu, Zhi-You; Bai, Fu-Sheng; Tian, Jing: Optimization methods for box-constrained nonlinear programming problems based on linear transformation and Lagrange interpolating polynomials (2017)
  6. Sagraloff, Michael; Mehlhorn, Kurt: Computing real roots of real polynomials (2016)
  7. Lawrence, Piers W.; Corless, Robert M.: Backward error of polynomial eigenvalue problems solved by linearization of Lagrange interpolants (2015)
  8. Wu, Z.Y.; Tian, J.; Ugon, J.: Global optimality conditions and optimization methods for polynomial programming problems (2015)
  9. Bini, Dario A.; Robol, Leonardo: Solving secular and polynomial equations: a multiprecision algorithm (2014)
  10. Nielsen, Johan Sejr Brinch; Simonsen, Jakob Grue: An experimental investigation of the normality of irrational algebraic numbers (2013)
  11. Liyun Dai, Bican Xia: logcf: An Efficient Tool for Real Root Isolation (2012) arXiv
  12. Pan, Victor Y.; Zheng, Ai-Long: Root-finding by expansion with independent constraints (2011)
  13. Pan, Victor Y.; Zheng, Ai-Long: New progress in real and complex polynomial root-finding (2011)
  14. Pan, V.Y.: Root-squaring with DPR1 matrices (2010)
  15. Pan, Victor Y.; Yan, Xiaodong: Additive preconditioning, eigenspaces, and the inverse iteration (2009)
  16. Pan, Victor Y.; Ivolgin, Dmitriy; Murphy, Brian; Rosholt, Rhys Eric; Taj-Eddin, Islam; Tang, Yuqing; Yan, Xiaodong: Additive preconditioning and aggregation in matrix computations (2008)
  17. Bini, Dario A.; Gemignani, Luca; Pan, Victor Y.: Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations (2005)
  18. Rouillier, Fabrice; Zimmermann, Paul: Efficient isolation of polynomial’s real roots. (2004)
  19. Fortune, Steven: An iterated eigenvalue algorithm for approximating roots of univariate polynomials (2002)