Die Gra kkarte als Parallelcomputer - Institut für Informatik
Die Gra kkarte als Parallelcomputer - Institut für Informatik
Die Gra kkarte als Parallelcomputer - Institut für Informatik
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A ∈ K m×n , B ∈ K n×p m, n, p ∈ N K ∈ {Rfloat32, Zint32}<br />
A· B =: C ∈ K m×p <br />
A =: (ai,j)i=1...m,j=1...n B C <br />
B <br />
<br />
r =1...m s=1...p m · p <br />
cr,s =<br />
n<br />
i=1<br />
ar,i · bi,s<br />
cr,s <br />
C <br />
n A B 1 <br />
C 2 · m · n · p m · p <br />
m · p O(n)<br />
cr,s <br />
cr,s <br />
A B <br />
w × w Cr,s C <br />
<br />
n/w <br />
Cr,s =<br />
i=1<br />
Ar,i · Bi,s<br />
A B<br />
⎛<br />
⎞ ⎛<br />
⎞<br />
× × × × B1,s ×<br />
⎛<br />
⎞<br />
× × ×<br />
⎝Ar,1<br />
. . . A n<br />
r, ⎠ ⎜ <br />
⎟<br />
· ⎝<br />
w × × ⎠ = ⎝ × Cr,s × ⎠<br />
× × ×<br />
× × × ×<br />
× B n<br />
w ,s<br />
<br />
w × w w | m, n, p <br />
C m p<br />
w × w <br />
<br />
<br />
w = 16 16 2 = 256
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