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JuliaApproximation / ApproxFun.jl

Julia package for function approximation
http://juliaapproximation.github.io/ApproxFun.jl/
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Implement proper colleaguebalance! #135

Open dlfivefifty opened 9 years ago

dlfivefifty commented 9 years ago

Should probably be 2^k scaling.

Two papers on the subject of balancing (companion only) are: http://www.siam.org/meetings/la03/proceedings/lemonnid.pdf

Another paper related to colleague matrices: http://eprints.ma.man.ac.uk/2182/01/covered/MIMS_ep2014_49.pdf

ajt60gaibb commented 9 years ago

Got to use QZ for numerical stability, which should automatically balance for you(?). This requires writing things as a generalized eigenvalue problem. Yet, I do think Vanni, Yuji, or any members of the Chebfun team would recommend QR for everyday use.

dlfivefifty commented 9 years ago

The reason I had to write my own colleaguebalance! Was to use LAPacks Hessenberg eigvals routine. (LAPacks standard eigvals does balancing automatic but the faster Hessenberg routine does not.). I'd expect QZ to be even slower than just using the standard eigvals.

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On 17 Apr 2015, at 10:50 pm, Alex Townsend notifications@github.com wrote:

Got to use QZ for numerical stability, which should automatically balance for you(?). This requires writing things as a generalized eigenvalue problem. Yet, I do think Vanni, Yuji, or any members of the Chebfun team would recommend QR for everyday use.

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