Lecture21 - IE 495 Lecture 21 Reading for This Lecture...

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IE 495 Lecture 21 November 14, 2000
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Reading for This Lecture Primary Miller and Boxer, Pages 124-128 Forsythe and Mohler, Sections 1 to 8
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Matrix Multiplication The standard sequential algorithm for multiplying matrices is O(n 3 ) . Strassen's Algorithm is a divide and conquer approach. Analysis of Strassen's Algorithm T( n ) = 7T( n /2) + dn 2 T( n ) = O( n log(7) ) = O( n 2.81... ) Every algorithm must be ( n 2 ) . The best known algorithm to date is O( n 2.376... ) . Can we parallelize Strassen's Algorithm?
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Parallel Matrix Multiplication Assume a CREW shared-memory architecture with n 3 processors. Label processors as P 111 through P nnn . Processor P ijk calculates a ik b kj . The remaining sums can be computed in O(log n) using a semigroup operation. The running time is O(log n) . Cost optimality?
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Matrix Multiplication on a Mesh Assume a 2n × 2n mesh computer. Assume each processor initially stores one entry. Algorithm Analysis Optimality
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Real Vector Spaces A real vector space is a set V , along with an addition operation that is commutative and associative.
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