On sunflowers and matrix multiplication

Lectures 1 and 2 Matrix Multiplication and Matrix Inversion 1 Prior Work on Matrix Multiplication

There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved t...

Matrix-Matrix Multiplication on Heterogeneous Platforms

Matrix Multiplication on Heterogeneous Platforms

ÐIn this paper, we address the issue of implementing matrix multiplication on heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collections of heterogeneous clusters. Intuitively, the problem is to load balance the work with different speed resources while minimizing the communication volume. We formally sta...

A New Parallel Matrix Multiplication Method Adapted on Fibonacci Hypercube Structure

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...

Matrix Multiplication on Hypercubes Using Full Bandwidth and Constant Storage Matrix Multiplication on Hypercubes Using Full Bandwidth and Constant Storage

For matrix multiplication on hypercube multiproces-sors with the product matrix accumulated in place a processor must receive about P 2 = p N elements of each input operand, with operands of size P P distributed evenly over N processors. With concurrent communication on all ports, the number of element transfers in sequence can be reduced to P 2 = p N logN for each input operand. We present a t...