Lecture21

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

This preview shows pages 1–7. Sign up to view the full content.

IE 495 Lecture 21 November 14, 2000

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Reading for This Lecture Primary Miller and Boxer, Pages 124-128 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 ( n 2 ) . The best known algorithm to date is O( n 2.376... ) . Can we parallelize Strassen's Algorithm?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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?
Matrix Multiplication on a Mesh Assume a 2n × 2n mesh computer. Assume each processor initially stores one entry. Algorithm Analysis Optimality

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Real Vector Spaces A real vector space is a set V , along with an addition operation that is commutative and associative.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern