Abstract
Sparse Matrix Vector Multiplication (SpMV) is one of the most basic problems in scientific and engineering computations. It is the basic operation in many realms, such as solving linear systems or eigenvalue problems. Nowadays, more than 90 percent of the world’s highest performance parallel computers in the top 500 use multicore architecture. So it is important practically to design the efficient methods of computing SpMV on multicore parallel computers. Usually, algorithms based on compressed sparse row (CSR) format suffer from a number of nonzero elements on each row so hardly as to use the multicore structure efficiently. Compressed Sparse Block (CSB) format is an effective storage format which can compute SpMV efficiently in a multicore computer. This paper presents a parallel multicore CSB format and SpMV based on it. We carried out numerical experiments on a parallel multicore computer. The results show that our parallel multicore CSB format and SpMV algorithm can reach high speedup, and they are highly scalable for banded matrices.
Highlights
With the development of science and technology, people need to deal with the increasing scale of the problems, which leads to the increasing computational overhead
We provides an overview of the Compressed Sparse Block (CSB) sparse-matrix storage format and describe the multicore sparse matrix-vector multiplication (SpMV) algorithm and its extension to parallel computer
Assuming that the matrix is stored in columns, the following algorithm can be used: a) Partition the matrix by columns with load balance, send the sub-matrix to the appropriate processor b) On the respective processor, sub-matrix need be converted into a matrix in CSB format c) Get the right part of the vector which will be multiplied d) Use SpMV in CSB format to compute the result Notice that the result of the second algorithm is still stored in each processor in distribution. 3.2
Summary
With the development of science and technology, people need to deal with the increasing scale of the problems, which leads to the increasing computational overhead. (2014) Parallel Multicore CSB Format and Its Sparse Matrix Vector Multiplication. All of TOP 500 supercomputers have been cluster structures, more than 90 percent of which have a multicore structure with at least 4 cores in 1 CPU [1] This means that how to improve the SpMV kernel in multicore parallel computers is crucial to raise the parallel performance and parallel efficiency. CSB format, which is proposed in 2009, can store a sparse matrix with a similar storage usage as CSR format [5] This format, designed for the multicore computer, can maintain load balance dynamically. The remainder of the paper is organized as follows: Section 2 introduces the basic CSB format and its SpMV method.
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