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# durand-kerner

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.

# Example

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")
}
``````

### Output

`````` 1.618033988749895+0i
-0.6180339887498949+0i
``````

# Install

Install using npm:

``````npm install durand-kerner
``````

# API

#### `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.