Suppose you want to multiply several matrices of various (compatible) sizes, A×B×C×D×E×F. How many operations... Suppose you want to multiply several matrices of various (compatible) sizes, A×B×C×D×E×F. How many operations will it take? A little thought tells you that if you have just two matrices A and B of size a×b and b×c respectively then it will take a⋅b⋅c operations to do the multiplication A×B. It turns out, though, that if you want to compute A×B×C×D×E×F, the number of operations it will take you depends on how you associate the matrices, that is, where you put parentheses. If you are writing a computer program that spends a lot of time multiplying several matrices together, you want to design your program so that it minimizes the number of operations it takes to do the multiplications. Its not too hard to come up with examples of matrices A×B×C×D×E×F for which the optimal choice of parentheses results in fewer operations than it takes to compute A×B!+abhi shelat uses this problem to illustrate dynamic programming to his algorithms class. Its a really cute example with a surprising result. I love computer science.
Posted on: Sun, 19 Oct 2014 08:59:49 +0000
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