Sherman - Morrison high-performance algorithm for inverse matrix on GPU

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