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: 19 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 (about 10 years ago)
• Default Branch: master
• Last Pushed: 2022-06-20T10:53:16.000Z (over 2 years ago)
• Last Synced: 2024-10-11T14:51:43.349Z (27 days ago)
• Language: Julia
• Size: 101 KB
• Stars: 15
• Watchers: 6
• 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

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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

```