Implementation of QR and LQ decompositions on shared memory parallel computing systems

Abstract

The paper presents some results of research of applicability of various computing schemes of implementing QR and LQ matrix decompositions for shared memory parallel systems. Three computational schemes to perform the Hauseholder transformations on shared memory parallel systems are considered: the right multiplication of the source matrix by the reflection matrix (QR decomposition) with column processing source matrix, the right multiplication (QR decomposition) with row processing source matrix, the left multiplication of the source matrix by the reflection matrix (LQ decomposition) with row processing source matrix. The results of numerical experiments estimating the speedup and efficiency of investigated computational schemes, their scalability on shared memory systems are presented, providing guidance on the choice of a particular computational scheme based on the characteristics of the original problem.