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

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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

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  • 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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