SHERMAN – MORRISON HIGH-PERFORMANCE ALGORITHM FOR INVERSE MATRIX ON GPU

Abstract

Matrix inversion is widely used in numerical methods, such as linear solvers, preconditioning
for linear system, domain decomposition, digital image processing, etc. High-performance
implementation of matrix inversion requires efficient matrix storage formats and optimal
distribution of computations between computing devices. In this paper, we study the performance
of traditional matrix inversion algorithms, such as LU-factorization and Gauss-Jordan, as well as
the conjugate gradient method and the Sherman – Morrison formula. In the last two algorithms,
matrix-vector products and scalar products are efficiently executed on multicore/manycore
processors. We compare the performance of the algorithms on hybrid multi-CPU multi-GPU
platforms, using the matrices from well-know test suites and from the numerical simulation of
wrap spring.