Multiplicação de matrizes comprimidas

Abstract

This work explores the field of Compressed Linear Algebra, which investigates methods for compressing matrices, enabling algebraic operations to be performed directly on the compressed representations efficiently. An algorithm for matrix compression was implemented, along with a method for multiplying compressed matrices by a right-hand vector, both based on the solution presented in Ferragina et al. (2022). The compression process was carried out in a partitioned manner, dividing the matrices into blocks processed sequentially. The experiments evaluated the impact of the number of blocks on reducing RAM memory usage. The results indicated a significant reduction in memory consumption during both compression and multiplication as the number of blocks used for matrix segmentation increased. Execution time improved during compression and remained nearly constant during multiplication. However, the compression rate experienced a moderate degradation as the number of blocks used to divide each matrix increased. We conclude that the proposed approach is promising for scenarios with limited computational resources, such as embedded devices and IoT.