We expose a systematic approach for developing distributed memory parallel matrix-matrix multiplication algorithms.

Aug 7, 2017 · In this article, we will look into methods that could optimize matrix multiplication in several ways. At the end we are going to analyze the performance of Traditional Matrix...

Jan 24, 2023 · Matrix multiplication is a fundamental operation in computer science, and it’s also an expensive one. In this article, we’ll explore how to optimize the operation for parallelism and locality by looking at different algorithms for matrix multiplication.

Assume that 3 processes are available for multiplying two × matrices. Then each of the 3 processes is assigned a single scalar multiplication. The additions for all can be carried out simultaneously in log steps each. Arrange 3 processes in a three-dimensional × × logical array.

Mar 1, 2017 · Regularity of data organization and operations carried out on data: data are organized in two-dimensional structures (the same matrices), and the operations basically consist of multiplication and addition. Foster 1-D matrix data decomposition. 1) …

Based on a suggestion by Professor Edelman, I decided to compare the parallel performance of matrix multiplication for pairs of regular matrices, and for pairs of irregular matrices.

In this section, we discuss how matrix and vector distribution can be linked to parallel 2D matrix-vector multiplication and rank-1 update operations, which then allows us to eventually describe the stationary C, A, and B2D algorithms for matrix-matrix multiplication that are part of the Elemental library. 2.1 Collective communication

Oct 22, 2020 · There are two main contendors for distributed memory matrix-matrix multiply: SUMMA and Cannon’s algorithm. But these are a little complicated, and maybe it’s worth first describing a simpler algorithm as a straw man.

For simplicity, we will work with square matrices of size n x n. Considered the number of processors available in parallel machines as p. The matrixes to multiply will be A and B. Both will be treated as dense matrices (with few 0's), the result will be stored it in the matrix C.

We expose a systematic approach for developing distributed-memory parallel matrix-matrix multiplication algorithms.