allanh@netcom.COM (Allan N. Hessenflow) (04/09/91)
I've been told that there's a way to factor the following matrix so that,
when it's multiplied by a column vector, the total number of multiplications
are reduced (2:1?) at the expense of some additions. However, I can't see
how. Any insights would be appreciated.
c3 -c5 c1 -c7
c5 c3 -c7 -c1
-c7 c1 c3 c5
c1 c7 -c5 c3
where cn=cos(n*pi/16).
allan
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Allan N. Hessenflow {apple|claris}!netcom!allanh allanh@netcom.comallanh@netcom.COM (Allan N. Hessenflow) (04/10/91)
In article <1991Apr8.200939.5533@netcom.COM>, I write: > I've been told that there's a way to factor the following matrix so that, > when it's multiplied by a column vector, the total number of multiplications > are reduced (2:1?) at the expense of some additions. However, I can't see > how. Any insights would be appreciated. > > c3 -c5 c1 -c7 > c5 c3 -c7 -c1 > -c7 c1 c3 c5 > c1 c7 -c5 c3 > > where cn=cos(n*pi/16). Everyone can stop thinking about this; I've figured it out (after receiving three replies to my posting, all of which say it's clearly impossible!). In case you're curious, I can't reduce the multiplies 2:1, but I can reduce it to 10 from the original 16. allan -- Allan N. Hessenflow {apple|claris}!netcom!allanh allanh@netcom.com