Eigensolve

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 25 articles )

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  1. De Terán, Fernando; Hernando, Carla: A note on generalized companion pencils in the monomial basis (2020)
  2. Feng, Lihua; Lu, Lu; Réti, Tamás; Stevanović, Dragan: A bound on the spectral radius of graphs in terms of their Zagreb indices (2020)
  3. García-Zapata, Juan Luis; Díaz Martín, Juan Carlos; Cortés Fácila, Álvaro: An adaptive subdivision method for root finding of univariate polynomials (2019)
  4. 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)
  5. Assis, M.; Jacobsen, J. L.; Jensen, I.; Maillard, J.-M.; McCoy, B. M.: Analyticity of the Ising susceptibility: an interpretation (2017)
  6. Pan, Victor Y.; Tsigaridas, Elias: Accelerated approximation of the complex roots and factors of a univariate polynomial (2017)
  7. Pan, Victor Y.; Zhao, Liang: Real polynomial root-finding by means of matrix and polynomial iterations (2017)
  8. Schleicher, Dierk; Stoll, Robin: Newton’s method in practice: finding all roots of polynomials of degree one million efficiently (2017)
  9. 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)
  10. Sagraloff, Michael; Mehlhorn, Kurt: Computing real roots of real polynomials (2016)
  11. Lawrence, Piers W.; Corless, Robert M.: Backward error of polynomial eigenvalue problems solved by linearization of Lagrange interpolants (2015)
  12. Wu, Zhiyou; Tian, Jing; Ugon, Julien; Zhang, Liang: Global optimality conditions and optimization methods for constrained polynomial programming problems (2015)
  13. Wu, Z. Y.; Tian, J.; Ugon, J.: Global optimality conditions and optimization methods for polynomial programming problems (2015)
  14. Bini, Dario A.; Robol, Leonardo: Solving secular and polynomial equations: a multiprecision algorithm (2014)
  15. Nielsen, Johan Sejr Brinch; Simonsen, Jakob Grue: An experimental investigation of the normality of irrational algebraic numbers (2013)
  16. Liyun Dai, Bican Xia: logcf: An Efficient Tool for Real Root Isolation (2012) arXiv
  17. Pan, Victor Y.; Zheng, Ai-Long: Root-finding by expansion with independent constraints (2011)
  18. Pan, Victor Y.; Zheng, Ai-Long: New progress in real and complex polynomial root-finding (2011)
  19. Pan, V. Y.: Root-squaring with DPR1 matrices (2010)
  20. Pan, Victor Y.; Yan, Xiaodong: Additive preconditioning, eigenspaces, and the inverse iteration (2009)

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