Support with JuliaIntervals?

[jarroyoe]

I have a function that requires finding a root using Roots.jl to give me a value. However, when I try to find all the roots using a package such as IntervalRootFinding.jl, my code gives me the following error:

ERROR: Roots.ConvergenceFailed("Algorithm failed to converge")

After debugging, the problem seems to be that the Roots functions are failing to handle the JuliaIntervals objects properly. I was wondering if there's a way to use this correctly, or if there's an alternative to using JuliaIntervals. Here's a MVE:

using Roots
using IntervalRootFinding

function f((x,y))
    g(z) = z^2-x
    z0 = find_zero(g,2)

    return SVector(x+y-z0,y+x-1)
end
X = IntervalBox(0..1,2)
roots(f,X)

[jverzani]

I’d have to see, but my guess is you’d be better served with the IntervalRoot Finding.jl package.

On Thu, Jul 14, 2022 at 2:27 PM Jorge Arroyo-Esquivel < ***@***.***> wrote: I have a function that requires finding a root using Roots.jl to give me a value. However, when I try to find all the roots using a package such as IntervalRootFinding.jl, my code gives me the following error: ERROR: Roots.ConvergenceFailed("Algorithm failed to converge") After debugging, the problem seems to be that the Roots functions are failing to handle the JuliaIntervals objects properly. I was wondering if there's a way to use this correctly, or if there's an alternative to using JuliaIntervals. Here's a MVE: using Roots using IntervalRootFinding function f((x,y)) g(z) = z^2-x z0 = find_zero(g,2) return SVector(x+y-z0,y+x-1) end X = IntervalBox(0..1,2) roots(f,X) — Reply to this email directly, view it on GitHub <#317>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AADG6TCCOAIFWAVBDNGP7CTVUBL2HANCNFSM53TEX33Q> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

-- John Verzani Chair, University Faculty Senate https://www1.cuny.edu/sites/cunyufs/ and Department of Mathematics College of Staten Island, CUNY

[jarroyoe]

I've tried transforming my code into a code supported by IntervalRootFinding, independent of Roots. In that case the roots that are found inside the function (z0 in my MVE) are intervals, and there seems to be issues regarding those roots.

Is there a way to use this package to find roots of multidimensional systems?

[jverzani]

Roots.jl is only for function f: R -> R, nothing multidimensional. As for your problem, it seems you have a function which returns an interval, so you'd need to have some stopping criteria to adjust for that. (small diameter that depends on the size of the interval in f?) I tried using IntervalRootFinding.roots and don't get anything working if I start nearby, but do if I start at the answer, so there is something at play here that can maybe be adapted for your problem.

julia> f(x) = x^2 - Interval(2,2.001)
f (generic function with 1 method)

julia> f(√2)
[-0.001, 4.4409e-16]

julia> IntervalRootFinding.roots(f, Interval(1.5))
Root{Interval{Float64}}[]

julia> IntervalRootFinding.roots(f, Interval(√2))
1-element Vector{Root{Interval{Float64}}}:
 Root([1.41421, 1.41422], :unknown)

[jarroyoe]

Thank you, it seems also that IntervalRootFinding is not capable at this moment of reliably using intervals as parameters to find roots. I ended up finding a workaround using a method that reduces my system to a 1D system and using the find_zeros function of Roots.