Algorithm Strassen's Method

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Strassen’s method

2B

: Strassen's method
n 2

n 2 ?

1
(A12 B12 1 A21 B21 1)

A11*B11 Strassen

n<=8 Strassen’s method
n3

M1~M7 :

MX (M1
A11+A22 B11+B22)

Strassen's method MX

MX+1

: m(n)=9*m(n/2)+3*n2

(n/2,n/4...etc)

M1~M7 (M1~M7 )
n*n
lg n
f(n)=∑ 9*(n/(2k))2 + 2*n2 + Θ(lg n) = Θ(n2)
k=1

: Pentium D 3.00GHz / Freebsd 7.0-RELEASE 32bit / gcc 4.2.1

n3 n

python :

n -100~100

n Strassen’s method n3

Strassen’s method n=120~130

n f(n) = 7*f(n/2)

n3 Strassen
Orz.........

not pure Strassen’s method?

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Algorithm Strassen's Method

1. Strassen’s method 2B

2. : Strassen's method n 2 n 2 ? 1 (A12 B12 1 A21 B21 1) A11*B11 Strassen

3. n<=8 Strassen’s method n3 M1~M7 : MX (M1 A11+A22 B11+B22) Strassen's method MX MX+1

4. : m(n)=9*m(n/2)+3*n2 (n/2,n/4...etc) M1~M7 (M1~M7 ) n*n lg n f(n)=∑ 9*(n/(2k))2 + 2*n2 + Θ(lg n) = Θ(n2) k=1

5. : Pentium D 3.00GHz / Freebsd 7.0-RELEASE 32bit / gcc 4.2.1 n3 n python : n -100~100

6.

7.

8.

9.

10. n Strassen’s method n3 Strassen’s method n=120~130 n f(n) = 7*f(n/2) n3 Strassen Orz......... not pure Strassen’s method?