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Unformatted text preview: IE 495 Lecture 21 November 14, 2000 Reading for This Lecture Primary ¡ Miller and Boxer, Pages 124128 ¡ Forsythe and Mohler, Sections 1 to 8 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 Ω ( n 2 ) . The best known algorithm to date is O( n 2.376... ) . Can we parallelize Strassen's Algorithm? Parallel Matrix Multiplication Assume a CREW sharedmemory 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? Matrix Multiplication on a Mesh Assume a 2n × 2n mesh computer....
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This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .
 Fall '08
 Linderoth
 Operations Research

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