PARALLEL MATRIX MULTIPLICATION ON THE CONNECTION MACHINE

Parallel Matrix Multiplication on the Connection Machine

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 Kalman Filtering on the Connection Machine

A parallel algorithm for square root Kalman filtering is developed and implemented on the Connection Machine (CM). The algorithm makes efficient use of parallel prefix or scan operations which are primitive instructions in the CM. Performance measurements show that the CM filter runs in time linear in the state vector size. This represents a great improvement over serial implementations which r...

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...

Scalable Parallel Matrix Multiplication on Distributed Memory Parallel Computers

Consider any known sequential algorithm for matrix multiplication over an arbitrary ring with time complexity O(N ), where 2 < 3. We show that such an algorithm can be parallelized on a distributed memory parallel computer (DMPC) in O(logN) time by using N = logN processors. Such a parallel computation is cost optimal and matches the performance of PRAM. Furthermore, our parallelization on a DM...