A FAST WAY TO COMPUTE MATRIX MULTIPLICATION MAE05 Presented by: - - PowerPoint PPT Presentation

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A FAST WAY TO COMPUTE MATRIX MULTIPLICATION MAE05 Presented by: - - PowerPoint PPT Presentation

Aug 08, 2023 14 likes β€’220 views

A FAST WAY TO COMPUTE MATRIX MULTIPLICATION MAE05 Presented by: Forrest Yau Zhen Kit , Jurong Pioneer Junior College 1 HIGHLIGHTS I. Background What led me to research more on this topic? II. Methodology How does my contributions help in

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A FAST WAY TO COMPUTE MATRIX MULTIPLICATION

Presented by: Forrest Yau Zhen Kit , Jurong Pioneer Junior College

1

MAE05

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2

HIGHLIGHTS

  • I. Background

What led me to research more on this topic?

  • II. Methodology

How does my contributions help in this research topic?

  • III. Conclusion

What are some future possible directions?

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  • I. BACKGROUND
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ο‚‘ It takes π‘œ3 steps to multiply two π‘œ Γ— π‘œ matrices. ο‚‘ Involves a total of 8 multiplication steps for a 2 x 2

matrices.

ο‚‘ However, it is not the most optimal method.

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NAÏVE MATRIX MULTIPLICATION

Can we go faster than π’πŸ’ ?

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STRASSEN’S ALGORITHM

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ο‚‘

𝑁1 = 𝑏11 + 𝑏22 𝑐11 + 𝑐22

ο‚‘

𝑁2 = 𝑏21 + 𝑏22 𝑐11

ο‚‘

𝑁3 = 𝑏11 𝑐12 βˆ’ 𝑐22

ο‚‘

𝑁4 = 𝑏22 𝑐21 βˆ’ 𝑐11

ο‚‘

𝑁5 = 𝑏11 + 𝑏12 𝑐22

ο‚‘

𝑁6 = 𝑏21 βˆ’ 𝑏11 𝑐11 + 𝑐12

ο‚‘

𝑁7 = 𝑏12 βˆ’ 𝑏22 𝑐21 + 𝑐22

STRASSEN’S ALGORITHM

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𝐷11 = 𝑁1 + 𝑁4 βˆ’ 𝑁5 + 𝑁7 𝐷12 = 𝑁3 + 𝑁5 𝐷21 = 𝑁2 + 𝑁4 𝐷22 = 𝑁1 βˆ’ 𝑁2 + 𝑁3 + 𝑁6 𝐡 = 𝑏11 𝑏12 𝑏21 𝑏22 𝐢 = 𝑐11 𝑐12 𝑐21 𝑐22 Where A x B = C= 𝑑11 𝑑12 𝑑21 𝑑22

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ο‚‘ Involves 7 multiplication steps instead of 8 multiplication

steps for a 2 x 2 matrices.

ο‚‘ Matrix multiplication algorithm efficiency of O(π‘œ2.81). ο‚‘ Faster compared to the naΓ―ve algorithm.

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STRASSEN'S ALGORITHM

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CAN WE GO FASTER THAN O(π‘œ2.81) ?

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  • II. METHODOLOGY
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ο‚‘ Inspiration from Gaussian elimination ο‚‘ Involves back-to-back elimination method to obtain a

β€œzero triangular form”

ο‚‘ An attempt to cut down the number of multiplication

steps to just 6

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PROPOSED ALGORITHM

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PERFORMANCE TEST I

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PERFORMANCE TEST I

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PERFORMANCE TEST II

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PERFORMANCE TEST II

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*Lower the bar, the better

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  • III. CONCLUSION
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ο‚‘ Matrix multiplication has its applications and uses in all

areas of study and purposes eg. Big Data, Data Representation.

ο‚‘ Cuts down the costs involved.

THE IMPORTANCE OF FAST MATRIX MULTIPLICATION ALGORITHM

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FUTURE DIRECTIONS

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ο‚‘ Requires further testing of proposed algorithm. ο‚‘ Basis of future research into achieving better

efficiency in other π‘œ Γ— π‘œ matrices.

ο‚‘ Possible use of Master Theorem to determine true

complexity.

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THAT’S THE END OF MY PRESENTATION THANK YOU!

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A FAST WAY TO COMPUTE MATRIX MULTIPLICATION

Summary of content covered:

  • NaΓ―ve matrix multiplication & Strassen’s algorithm
  • Possibility of achieving a more efficient algorithm
  • Importance of fast matrix multiplication

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MAE05

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PERFORMANCE TEST II

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ο‚‘ Benchmarks used to run the algorithm:

  • 1. CPU

 Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz

  • 2. GPU

 NVIDIA GeForce 940MX

  • 3. RAM

 8GB