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README.md

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@@ -8,9 +8,7 @@ A Julia repository for linear algebra with infinite banded and block-banded matr
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This currently supports the infinite-dimensional QR factorization for banded matrices, also known as the adaptive QR decomposition as the entries of the QR decomposition are determined lazily.
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As a simple example, consider the Bessel recurrence relationship:
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$$
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J_{n-1}(z) - {2 n \over z} J_n(z) + J_{n+1}(z) = 0
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$$
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- <img src="https://latex.codecogs.com/gif.latex?O_t=J_{n-1}(z) - {2 n \over z} J_n(z) + J_{n+1}(z) = 0" />
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This can be recast as an infinite linear system:
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```julia
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julia> using InfiniteLinearAlgebra, InfiniteArrays, BandedMatrices, FillArrays, SpecialFunctions
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```
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The first row corresponds to specifying an initial condition. Thus we can determine $J_n(z)$ via solving the recurrence:
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The first row corresponds to specifying an initial condition. Thus we can determine the Bessel functions via solving the recurrence:
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```julia
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julia> A \ Vcat([besselj(1,z)], Zeros(∞))
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-element LazyArrays.CachedArray{Float64,1,Array{Float64,1},Zeros{Float64,1,Tuple{InfiniteArrays.OneToInf{Int64}}}} with indices OneToInf():

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