NTA-NET (UGC-NET) Computer Science & Applications (87) Analysis and Design of Algorithms-Divide & Conquer, and Partitioning Algorithms Study Material (Page 3 of 5)
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Complexity Analysis: Strassen Matrix Multiplication Algorithm
Karatsuba method reduces the multiplication operations by 1.
It leads to the following recurrence equation:
… (159 more equations) …
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Strassen Matrix Multiplication
- Volker Strassen is a German mathematician works on matrix multiplication that outperforms the general matrix multiplication algorithm.
- Using the Strassen algorithm, the multiplication of matrices A and B to yield matrix C can be carried out using seven multiplications.
This is shown by following formulas:
d1 = (A00 + A11) ⚹ (B00 + B11)
d2 = (A10 + A11) ⚹ B00
d3 = A00 ⚹ (B01-B11)
d4 = A11 ⚹ (B10-B00)
d5 = (A00 + A01) ⚹ B11
d6 = (A10-A00) ⚹ (B00 + B01)
d7 = (A01-A11) ⚹ (B10 + B11)
Resulting product matrix C are given as follows:
C11 = d1 + d4 − d5 + d7
C12 = d3 + d5
C21 = d2 + d4
C22 = d1 + d3 − d2 − d6
Divide and Conquer Method
- Divide a matrix of order recursively till …
… (267 more equations, 36 figures) …
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