Matrix Multiplication Chains Decision Sequence Problem State ...
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Matrix Multiplication Chains Decision Sequence Problem State ...
ƒ If the last matrix product is (M1x M2 x … xMk) x (Mk+1x. Mk+2 x … xMq), the
state becomes {(1,k), (k+1,q)}. Verify Principle Of Optimality. • Let Mij= Mi x Mi+1 x
...
Matrix Multiplication Chains • Determine the best way to compute the matrix product M1x M2 x M3 x … x Mq. • Let the dimensions of Mi be rix ri+1. • q-1 matrix multiplications are to be done. • Decide the matrices involved in each of these multiplications.
Decision Sequence • M1x M2 x M3 x … x Mq • Determine the q-1 matrix products in reverse order. What is the last multiplication? What is the next to last multiplication? And so on.
Problem State
Verify Principle Of Optimality
• M1x M2 x M3 x … x Mq • The matrices involved in each multiplication are a contiguous subset of the given q matrices. • The problem state is given by a set of pairs of the form (i, j), i
