a new parallel matrix multiplication method adapted on fibonacci hypercube structure

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...

Parallel Matrix Multiplication Algorithms on Hypercube Multiprocessors 1

In this paper, we present three parallel algorithms for matrix multiplication. The rst one, which employs pipelining techniques on a mesh grid, uses only one copy of data matrices. The second one uses multiple copies of data matrices also on a mesh grid. Although data communication operations of the second algorithm are reduced, the requirement of local data memory for each processing element i...

Parallel Matrix Multiplication on the Connection Machine

The Fibonacci hypercube

The Fibonacci Hypercube is defined as the polytope determined by the convex hull of the “Fibonacci” strings, i.e., binary strings of length n having no consecutive ones. We obtain an efficient characterization of vertex adjacency and use this to study the graph of the Fibonacci Hypercube. In particular we discuss a decomposition of the graph into self-similar subgraphs that are also graphs of F...

Parallel Sparse Matrix Multiplication for Linear Scaling Electronic Structure Calculations

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must be run on parallel computers. We analyse the problem of parallelising the multiplication of sparse matrices with the sparsity pattern required by linear-sca...

Highly Parallel Sparse Matrix-Matrix Multiplication

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on two-dimensional block distribution of sparse matrices where serial sections use a novel hyperspa...