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JuliaApproximation / ApproxFun.jl

Julia package for function approximation
http://juliaapproximation.github.io/ApproxFun.jl/
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Exploit structure in \ #95

Closed dlfivefifty closed 9 years ago

dlfivefifty commented 9 years ago

Examples:

1) upper triangular operators should use backsubstitution! 2) many operators decouple the even and odd rows/columns (E.g. Ultraspherical Derivative/Conversion). exploiting this halves the bandwidth which results in 1/4 the computational cost. 3) Should lower triangular operators use "forwardsubstition!"?

dlfivefifty commented 9 years ago

\ now exploits even/odd separation for large bandwidths.

This is disabled for now for PDEs as pdesolve() needs optimization

dlfivefifty commented 9 years ago

Another structure that is important is Dense matrix + Banded. Probably should work via LAPack QR on the dense columns to upper triangularize followed by adaptive qr.

Now addentries! can write to regular matrices so a dense solver is more practical