InfiniteLinearAlgebra.jl

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Cholesky decompositon of spd BandedBlockBanded matrices

1

How much work would it be to get cholesky working on infinite spd BandedBlockBanded matrices? I'm wondering whether decomposition methods also allow for interesting weight OPs in higher dimension and...

TSGut

dlfivefifty

Diagonality and bandedness checks with InfiniteArrays.jl?

5

The methods in InfiniteArrays.jl and InfiniteLinearAlgebra.jl don't currently seem to agree on what is a diagonal and what is a banded matrix. To give some concrete examples: A minimal working...

TSGut

Lanczos via Givens

11

I'm trying to [rewrite lanczos](https://github.com/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl/blob/f2068e48fbd7cae23ca471a0a8a5ba946426d3f9/test/runtests.jl#L9) (i.e. Stieltjes) in ∞-arrays which made me realise that it essentially boils down to tridiagonalising `W`, a symmetric positive definite matrix such that ```julia w...

dlfivefifty

Cholesky broken for diagonal matrices

1

```Julia julia> cholesky(Symmetric(BandedMatrix(0 => 1:∞))) Cholesky{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, BandedMatrix{Float64, ApplyArray{Float64, 2, typeof(*), Tuple{Matrix{Int64}, ApplyArray{Float64, 2, typeof(vcat), Tuple{ApplyArray{Float64, 2, typeof(hcat), Tuple{Zeros{Float64, 2, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, InfiniteArrays.ReshapedArray{Int64, 2, InfiniteArrays.InfUnitRange{Int64}, Tuple{Int64, Infinities.InfiniteCardinal{0}},...

dlfivefifty

The example in https://github.com/JuliaLinearAlgebra/InfiniteLinearAlgebra.jl/blob/master/examples/periodicschrodinger.jl is erroring out for me. MWE (same code, just not using `Plots`) ```julia using InfiniteLinearAlgebra A = BlockTridiagonal(Vcat([[0. 1.; 0. 0.]],Fill([0. 1.; 0. 0.], ∞)), Vcat([[-1....

MasonProtter

Support Transpose broadcasting

1

dlfivefifty

dlfivefifty

Related to https://github.com/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl/issues/68, I have a workaround for the problem described therein but it relies on being able to tell when a matrix is not positive definite, the standard test...

TSGut

Infinite UL factorisation

2

I wonder if something similar to #179 could be done for computing UL factorisations, i.e. $\mathbf X = \mathbf U\mathbf L$ for non-symmetric tridiagonal $\mathbf X$? Has much thought been...

DanielVandH