On 2016-05-19 10:56, Fred Lunnon wrote:
On 5/19/16, Warren D Smith <warren.wds@gmail.com> wrote:
it wouldn't let me post that to geometric-algebra, so you might want to post it there for me.
Or you could complain about how I'm wrong some more. I have not programmed this or tried to... but it still seems to me I'm obviously right plus was all along...
I'll take option 2, thanks. Screenshots of
listing (sans comments) of program implementing algorithms under discussion at
https://www.dropbox.com/s/3cr364xiw628i23/given_p0.tiff ;
output of column-by-column algorithm test result at
https://www.dropbox.com/s/uwsmq2habm4tfgp/given_p1.tiff ;
output of triangular algorithm test result at
https://www.dropbox.com/s/9v3t0nicq6huf2g/given_p2.tiff .
Observe that the first result is finally diagonal, whereas the second has nonzero first column. Apologies for the excessive precision, courtesy of yet another "feature". Maple source code in attached text file, should you wish to experiment.
I received the attachment! How?? --rwg
The procedures I gave will be stable in the sense numerical errors will grow like polynomial(N), as opposed to many procedures such as gaussian elimination with partial pivoting where error can grow exponentially(N) for unfriendly matrices.
Wilkinson famously showed gauss with complete pivoting is backwards stable in the sense of a certain bound on error growth, but I think his bound was superpolynomial although subexponential.
Good points about stability, which I shall pass on to GA list in due course.
Fred Lunnon