SingularIntegralEquations.jl
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Should OffHilbert/OffSingularIntegral store concrete data in low-rank form?
Banded linear algebra is arguably inapplicable to these operators, setting them on the path to being amenable to hierarchical solvers.
Should we also combine them with Hilbert/SingularIntegral and have them generated by a variation of the @calculus_operator macro?
There's a lot to be done with improving large bandwidth linear algebra. I think when the bandwidth is large,creating a dense matrix and using LAPack is much faster than ApproxFun's \