Review on Sparse Matrix Storage Formats With Space Complexity Analysis

Abstract

Sparse matrix-vector multiplication (SpMV) is a challenging computational kernel in linear algebra applications, like data mining, image processing, and machine learning. The performance of this kernel is greatly dependent on the size of the input matrix and the underlying hardware features. Various sparse matrix storage formats referred to commonly as sparse formats have been proposed in the literature to reduce the size of the matrix. In modern multi-core and many-core architectures, the performance of the kernel is mainly dependent on memory wall and power wall problem. Normally review on sparse formats is done with specific architecture or with specific application. This chapter presents a comparative study on various sparse formats in cross platform architecture like CPU, graphics processor unit (GPU), and single instruction multiple data stream (SIMD) registers. Space complexity analysis of various formats with its representation is discussed. Finally, the merits and demerits of each format have been summarized into a table.