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Optimal block size for matrix multiplication using blocking

Authors: Sasko Ristov; Marjan Gusev; Goran Velkoski;

Optimal block size for matrix multiplication using blocking

Abstract

Matrix multiplication is a widely used algorithm in today's computing. Speeding up the multiplication of huge matrices is imperative for scientists and they are trying to discover the fastest algorithm. Blocking the matrices reduces the cache misses since both blocks can be stored in L1 cache and thus only the first access of an element will result in cache miss and all other access will be a cache hit. However, choosing the block size is not the only optimization. In this paper we analyze the impact of various block size (M ·K and K ·N) on the performance. The realized experiments use different parameter values for K and predefined values of the parameters M and N, to test algorithm behavior in different cache regions. The results of the experiments show three phenomena. The first phenomenon is that if M is greater than N, then choosing the first block M ·N will achieve a significantly greater speed. The second states that, if the second parameter N is increased for constant M has no significant influence on the performance. Finally, the third phenomenon is that the speed decreases significantly if N is increasing for constant M.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
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