Find the zeros of a generalised Laguerre polynomial

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SUMMARY

The discussion focuses on finding the zeros of a generalized Laguerre polynomial, specifically the equation L^{\alpha}_N (x_i) = 0. Users reference two resources: a Fortran library available at https://people.sc.fsu.edu/~jburkardt/f77_src/laguerre_polynomial/laguerre_polynomial.f and a Fortran 90 source file from GitHub at https://github.com/exciting/exciting/blob/master/src/src_gw/gaulag.f90. The inquiry also includes a request for information regarding the relative accuracy of the zeros produced by these libraries.

PREREQUISITES
  • Understanding of generalized Laguerre polynomials
  • Familiarity with Fortran programming language
  • Knowledge of numerical methods for root-finding
  • Experience with polynomial approximation techniques
NEXT STEPS
  • Research the implementation of root-finding algorithms in Fortran
  • Explore the accuracy and performance of the Fortran library for Laguerre polynomials
  • Investigate numerical stability in polynomial root-finding
  • Learn about the properties and applications of generalized Laguerre polynomials
USEFUL FOR

Mathematicians, numerical analysts, and software developers working on polynomial computations and numerical methods for root-finding.

ognik
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Hi - does anyone know of a program library/subroutine - failing that some other source, to find the zeros of a generalised Laguerre polynomial? ie. ## L^{\alpha}_N (x_i) = 0 ##
 
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