CPOLY

Algorithm 419: zeros of a complex polynomial [C2] The subroutine CPOLY is a Fortran program to find all the zeros of a complex polynomial by the three-stage complex algorithm described in Jenkins and Traub [4]. (An algorithm for real polynomials is given in [5].) The algorithm is similar in spirit to the two-stage algorithms studied by Traub [1, 2]. The program finds the zeros one at a time in roughly increasing order of modulus and deflates the polynomial to one of lower degree. The program is extremely fast and the timing is quite insensitive to the distribution of zeros. Extensive testing of an Algol version of the program, reported in Jenkins [3], has shown the program to be very reliable. (Source: http://plato.asu.edu)

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 13 articles )

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  1. Chakraborty, A.; Gopalakrishnan, S.: A spectrally formulated finite element for wave propagation analysis in functionally graded beams. (2003)
  2. Chen, Zhidong; Mechefske, Chris K.: Diagnosis of machinery fault status using transient vibration signal parameters (2002)
  3. Zhang, Hong: Numerical condition of polynomials in different forms (2001)
  4. Pan, Victor Y.: Approximating complex polynomial zeros: modified Weyl’s quadtree construction and improved Newton’s iteration. (2000)
  5. Pan, Victor Y.: Solving a polynomial equation: Some history and recent progress (1997)
  6. Mertz, G.; Myers, R.A.: An augmented Clark model for stability of populations (1996)
  7. Toh, Kim-Chuan; Trefethen, Lloyd N.: Pseudozeros of polynomials and pseudospectra of companion matrices (1994)
  8. Liang, Zhipei; Haacke, E.Mark; Thomas, Cecil W.: High-resolution inversion of finite Fourier transform data through a localised polynomial approximation (1989)
  9. Abhyankar, Shreeram S.; Bajaj, Chanderjit: Automatic parametrization of rational curves and surfaces. II: Cubics and cubicoids (1987)
  10. Maeder, A.J.; Wynton, S.A.: Some parallel methods for polynomial root-finding (1987)
  11. Murphy, J.O.; Lopez, J.M.: The onset of oscillatory instability in a rotating layer of mercury heated from below and subject to a magnetic field (1986)
  12. Ganzha, V.G.; Mazurik, S.I.; Shapeev, V.P.: Symbolic manipulations on a computer and their application to generation and investigation of difference schemes (1985)
  13. Rodabaugh, D.J.; Thompson, Skip: Adams-type methods with increased ranges of stability (1978)