I am interested in computing a small proportion (between 3 and 10% of the matrix size) of the eigenvalues of a matrix with extended precision. As a toy example, let’s take the matrix A define by: T = Complex{Float128} N = 64 A = Tridiagonal(rand(T, N - 1), rand(T, N), rand(T, N - 1)) The following…

I think what you need in addition is using GenericSchur. At least this is what allows one to use ArnoldiMethod.jl with arbitrary float types. julia> using ArnoldiMethod, GenericSchur, DoubleFloats julia> T = Complex{Double64} Complex{Double64} julia> N = 64 64 julia> A = Tridiagonal(rand(T, N - …

You can get the job done with GenericLinearAlgebra.jl and ArnoldiMethod.jl: julia> partialschur(A; nev=round(Int, 0.1 * N), which=LM())[1] PartialSchur decomposition (Complex{Float128}) of dimension 6 eigenvalues: 6-element Vector{Complex{Float128}}: 1.76732917570178181966857786046259500e+00 + 1.8…

If you convert your Tridiagonal matrix to a general Matrix your code should work using GenericLinearAlgebra.eigvals: `` using LinearAlgebra, GenericLinearAlgebra, Quadmath, DoubleFloats complex_matrix(T,n) = rand(Complex{T}, n) * rand(Complex{T}, n)’ generic_tridiag(m) = Matrix(Tridiagonal(m)) n…

Can you elaborate on how you use the GenericLinearAlgebra.jl package from their GitHub I do not understand how to use it in my case.

Yes, I have already see that eigvals from the LinearAlgebra.jl works with extended precision (and you do not need the GenericLinearAlgebra.jl package for eigenvals to works) but the two mains issue with this method: It transform the tridiagonal matrix into a dense matrix which become prohibitive a…

Yes, I tried KrylovKit.jl in my second example (I have edited my post to be hopefully more clear). It is possible that I am not using it properly for what I want to do. I have seen that you can give it the product matrix-vector instead of the matrix but I did not manage to make it works with extend…

Thank you @fgerick for the answers. I have found the main issue which was that the ArnoldiMethod.jl package was pinned at version 0.1.0 because of BifurcationKit.jl. When I remove BifurcationKit.jl and update ArnoldiMethod.jl to 0.2.0 it worked. Actually, it even worked without GenericLinearAlgebr…

Ok thanks, I will edit: https://github.com/Jutho/KrylovKit.jl/issues/51

Eigenvalues and extended precision

Specific Domains Numerics

rveltz September 14, 2021, 8:53am 9

You should open an issue because it should be type agnostic

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Eigenvalues and extended precision

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