# strassen matrix multiplication algorithm

Description
1. Strassen's Matrix Multiplication Presented by: Ali Mamoon 07-0014 2. Contents  Matrix multiplication  Divide and Conquer  Strassen's idea …
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
• 1. Strassen's Matrix Multiplication Presented by: Ali Mamoon 07-0014
• 2. Contents  Matrix multiplication  Divide and Conquer  Strassen's idea  Analysis
• 3. Standard algorithm for i ←1 to n do for j←1 to n do cij←0 for k←1 to n do cij←cij+ aik⋅bkj N C i, j a i ,k bk , j k 1 N N N 3 3 Thus T ( N ) c cN O(N ) i1 j1k 1
• 4. Divide-and-Conquer  Divide-and conquer is a general algorithm design paradigm:  Divide: divide the input data S in two or more disjoint subsets S1, S2, …  Recur: solve the sub problems recursively  Conquer: combine the solutions for S1, S2, …, into a solution for S  The base case for the recursion are sub problems of constant size  Analysis can be done using recurrence equations
• 5. Matrix Multiplication through Divide and Conquer Approach
• 6. Divide-and-conquer algorithm
• 7. Master theorem
• 8. Strassen’s idea  Multiply 2×2matrices with only 7 recursive multiplications.  P1= a⋅(f–h) r=P5+ P4–P2+ P6 P2= (a+ b) ⋅h  s=P1+ P2 P3= (c+ d) ⋅e  t=P3+ P4  P4= d⋅(g–e) u=P5+ P1–P3–P7 P5= (a+ d) ⋅(e+ h)  P6= (b–d) ⋅(g+ h)  P7= (a–c) ⋅(e+ f )   Note:  7mults, 18adds/subs.  Note: No reliance on commutative of multiplication!
• 9. Strassen Algorithm void matmul(int *A, int *B, int *R, int n) { if (n == 1) { (*R) += (*A) * (*B); } else { matmul(A, B, R, n/4); matmul(A, B+(n/4), R+(n/4), n/4); matmul(A+2*(n/4), B, R+2*(n/4), n/4); matmul(A+2*(n/4), B+(n/4), R+3*(n/4), n/4); matmul(A+(n/4), B+2*(n/4), R, n/4); matmul(A+(n/4), B+3*(n/4), R+(n/4), n/4); matmul(A+3*(n/4), B+2*(n/4), R+2*(n/4), n/4); matmul(A+3*(n/4), B+3*(n/4), R+3*(n/4), n/4); Divide matrices in } sub-matrices and recursively multiply sub-matrices
• 10. Analysis of Strassen's  T(n) = 7T(n/2) + Θ(n2)  nlogba= nlog27≈n2.81  ⇒CASE1⇒T(n) = Θ(nlg7).  The number2.81may not seem much smaller than 3, but because the difference is in the exponent, the impact on running time is significant. In fact, Strassen’s algorithm beats the ordinary algorithm on today’s machines for n≥32or so.  Best to date (of theoretical interest only): Θ(n2.376…)

Jul 23, 2017

#### Control Your Halloween Decorations With Arduino

Jul 23, 2017
Search
Similar documents

### Stegnography of High Embedding Efficiency by Using an Extended Matrix Encoding Algorithm

View more...
Related Search