Thread View: comp.dsp
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Started by Allan N. Hessenflow
Mon, 08 Apr 1991 20:09
factoring matrices question
Author: Allan N. Hessenflow
Date: Mon, 08 Apr 1991 20:09
Date: Mon, 08 Apr 1991 20:09
16 lines
838 bytes
838 bytes
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
--
Allan N. Hessenflow {apple|claris}!netcom!allanh allanh@netcom.com
Re: factoring matrices question
Author: Allan N. Hessenflow
Date: Wed, 10 Apr 1991 05:14
Date: Wed, 10 Apr 1991 05:14
24 lines
1261 bytes
1261 bytes
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
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