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Divide and Conquer Matrix Multiplic ation Design and Analysis of Algorithms I

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Following material on Algorithms Part I, Week 1

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Page 1: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Divide and ConquerMatrix Multiplication

Design and Analysis of Algorithms I

Page 2: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

Matrix Multiplication

Page 3: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

Example (n=2)

Page 4: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

𝜃 ¿𝜃(𝑛2)

𝜃(𝑛3)

𝜃(𝑛4)

What is the asymptotic running time of the straightforward iterative algorithm for matrix multiplication?

Page 5: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

The Divide and Conquer Paradigm

Page 6: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

Applying Divide and Conquer

Page 7: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

Recursive Algorithm #1

Page 8: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

Strassen’s Algorithm (1969)

Page 9: Completed Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PPT for Strassen's Subcubic Matrix Multiplication Algorithm (22 min) PDF for Strassen's Subcubic Matrix Multiplication

Tim Roughgarden

The Details


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