https://github.com/andreasnoack/fastpolynomialroots.jl

Fast and backward stable computation of roots of polynomials in Julia
https://github.com/andreasnoack/fastpolynomialroots.jl

Last synced: 3 days ago
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Fast and backward stable computation of roots of polynomials in Julia

• Host: GitHub
• URL: https://github.com/andreasnoack/fastpolynomialroots.jl
• Owner: andreasnoack
• License: mit
• Created: 2014-08-25T23:31:47.000Z (almost 11 years ago)
• Default Branch: master
• Last Pushed: 2025-05-18T20:28:46.000Z (about 2 months ago)
• Last Synced: 2025-05-18T21:22:01.589Z (about 2 months ago)
• Language: Julia
• Size: 111 KB
• Stars: 17
• Watchers: 5
• Forks: 4
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# FastPolynomialRoots.jl - Fast and backward stable computation of roots of polynomials

[![CI](https://github.com/andreasnoack/FastPolynomialRoots.jl/actions/workflows/CI.yml/badge.svg)](https://github.com/andreasnoack/FastPolynomialRoots.jl/actions/workflows/CI.yml)

[![codecov](https://codecov.io/gh/andreasnoack/FastPolynomialRoots.jl/graph/badge.svg?token=mALbv2gzq2)](https://codecov.io/gh/andreasnoack/FastPolynomialRoots.jl)

This package is a Julia wrapper of the Fortran programs accompanying [Fast and Backward Stable Computation of Roots of Polynomials](http://epubs.siam.org/doi/abs/10.1137/140983434) by Jared L. Aurentz, Thomas Mach, Raf Vandebril and David S. Watkins.

## Usage

The package provides the unexported function `FastPolynomialRoots.rootsFastPolynomialRoots(p::Vector{<:Union{Float64,Complex{Float64}}})`

which computes the roots of the polynomial `p[1] + p[2]*x + p[3]*x^2 + ... + p[k]*x^(k-1)`. The package also overwrites the `roots(::Polynomial)` methods in the `Polynomials` package for `Float64` and `Complex{Float64}` elements with the fast versions provided by this package. See the examples below.

## Example 1: Speed up `roots`

```julia

julia> using Polynomials, BenchmarkTools

julia> @btime roots(p) setup=(p = Polynomial(randn(500)));

  223.135 ms (23 allocations: 3.97 MiB)

julia> using FastPolynomialRoots

julia> @btime roots(p) setup=(p = Polynomial(randn(500)));

  30.786 ms (7 allocations: 26.41 KiB)

```

## Example 2: Roots of a polynomial of degree 10,000

A computation of this size would not be feasible on a desktop with the traditional method

but can be handled by FastPolynomialRoots.

```julia

julia> using Polynomials, BenchmarkTools, FastPolynomialRoots

julia> n = 10000;

julia> r = @btime roots(p) setup=(p = Polynomial(randn(n + 1)));

  10.290 s (13 allocations: 508.38 KiB)

julia> sum(isreal, r)

7

julia> 2/π*log(n) + 0.6257358072 + 2/(n*π) # Edelman and Kostlan

6.489284260212659

```