Abstract
This paper presents a Monte Carlo SPAI pre-conditioner. In contrast to the standard deterministic SPAI pre-conditioners that use the Frobenius norm, a Monte Carlo alternative that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough matrix inverse (MI) is given. Monte Carlo methods enable a quick rough estimate of the non-zero elements of the inverse matrix with a given precision and certain probability. The advantage of this method is that the same approach is applied to sparse and dense matrices and that complexity of the Monte Carlo matrix inversion is linear of the size of the matrix. The behaviour of the proposed algorithm is studied, its performance is investigated and a comparison with the standard deterministic SPAI, as well as the optimized and parallel MSPAI version is made. Further Monte Carlo SPAI and MSPAI are used for solving systems of linear algebraic equations (SLAE) using BiCGSTAB and a comparison of the results is made.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
