mersenneforum.org Karatsuba algorithm relation to Matrix Multiplication (Strassen Algorithm)?
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 2019-07-29, 19:56 #1 neomacdev   Apr 2019 2×11 Posts Karatsuba algorithm relation to Matrix Multiplication (Strassen Algorithm)? Hi, This question is not Mersenne prime related, nor prime related at all. There is a series of optimized algorithms for Matrix Multiplication ala Strassen's Algorithm for performing 2x2 x 2x2 Matrix multiplication in only 7 scalar multiplications rather than the standard 8. And there is Karatsuba's algorithm for performing large integer multiplication which reduces the number of single digit multiplications from n^2 to n^1.58. I vaguely recall I saw a reference to a Mathematics paper that, if I recall correctly, stated for every Strassen-like accelerated matrix multiplication algorithm there was a corresponding accelerated integer multiplication algorithm like Karatsuba. Is anyone framiliar with this paper? Can you provide a citation or link? I have tried searching, but must not be using the correct terms as I can't locate it. Or perhaps I've imagined the entire thing! Thanks. For reference: Strassen's Algorithm https://en.wikipedia.org/wiki/Strassen_algorithm Karatsuba's Algorithm https://en.wikipedia.org/wiki/Karatsuba_algorithm
2019-07-30, 01:40   #2
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Quote:
 Originally Posted by neomacdev Hi, This question is not Mersenne prime related, nor prime related at all. There is a series of optimized algorithms for Matrix Multiplication ala Strassen's Algorithm for performing 2x2 x 2x2 Matrix multiplication in only 7 scalar multiplications rather than the standard 8. And there is Karatsuba's algorithm for performing large integer multiplication which reduces the number of single digit multiplications from n^2 to n^1.58. I vaguely recall I saw a reference to a Mathematics paper that, if I recall correctly, stated for every Strassen-like accelerated matrix multiplication algorithm there was a corresponding accelerated integer multiplication algorithm like Karatsuba. Is anyone framiliar with this paper? Can you provide a citation or link? I have tried searching, but must not be using the correct terms as I can't locate it. Or perhaps I've imagined the entire thing! Thanks. For reference: Strassen's Algorithm https://en.wikipedia.org/wiki/Strassen_algorithm Karatsuba's Algorithm https://en.wikipedia.org/wiki/Karatsuba_algorithm
I'm not sure about the paper to which you refer but have you looked at Toom-3?
It reduces 9 multiplies to 5.
Wikipedia has a good article under the algorithm's full name: Toom-Cook.
Also, check the link the article has to Marco Bodrato's web site. He has some good stuff.
The freely available big integer system call LibTomMath has a Toom-3 implementation also.

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