Extending the Gauss–Huard method for the solution of Lyapunovrnmatrix equations and matrix inversion

摘要

The solution of linear systems is a recurrent operation in scientific and engineering applications, traditionallyrnaddressed via the LU factorization. The Gauss–Huard (GH) algorithm has been introduced as an efficientrnalternative in modern platforms equipped with accelerators, although this approach presented some functionalrnconstraints. In particular, it was not possible to reuse part of the computations in the solution of delayedrnlinear systems or in the inversion of the matrix. Here, we adapt GH to overcome these two deficienciesrnof GH, yielding new algorithms that exhibit the same computational cost as their corresponding counterpartsrnbased on the LU factorization of the matrix. We evaluate the novel GH extensions on the solution ofrnLyapunov matrix equations via the LRCF-ADI method, validating our approach via experiments with threernbenchmarks from model order reduction.