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durand-kerner v1.0.0

Finds multiple roots of polynomials using Weierstrass' method


Finds all the roots of a polynomial by Weierstrass' method (or known in Abramowitz&Stegun as the Durand-Kerner method). This is basically a generalization of Newton's method that works for multiple roots.

build status


To find the roots for 1 + 1*x - 1*x^2:

var findRoots = require("durand-kerner")

var roots = findRoots([1, 1, -1])

// Now:
//      roots[0] = real part of roots
//      roots[1] = imaginary part of roots

for(var i=0; i<roots.length; ++i) {
  console.log(roots[0][i] + "+" + roots[1][i] + "i")




Install using npm:

npm install durand-kerner


require("durand-kerner")(r_coeff[, i_coeff, n_iters, tolerance, initial])

Finds the roots of a polynomial whose real coefficients are given by r_coeff and imaginary coefficients by i_coeff.

  • r_coeff - the real part of the polynomial's coefficients, stored in an array
  • i_coeff - the imaginary part of the polynomial's coefficients (default all 0)
  • n_iters - Maximum number of iterations to run before bailout. Default is 100 * n * n
  • tolerance - Stopping threshold. Default is 1e-6
  • initial - Initial guess for solution vector (must have the same length as r_coeff). This also gets the solution (optional)

Returns An array of roots.


(c) 2013 Mikola Lysenko. MIT License


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