An EM-based iterative method for solving large sparse linear systems

ABSTRACT

We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise, convergence to a minimal Kullback–Leibler divergence point is guaranteed. The algorithm is easy to code and competitive with other iterative algorithms.

KEYWORDS:

• EM algorithm
• indefinite matrix
• iterative method
• Kullback–Leibler divergence
• sparse linear system

AMS/MSC SUBJECT CLASSIFICATION:

• 65F10

Acknowledgements

The authors are grateful for the reviewer's helpful comments on a previous version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Minwoo Chae  http://orcid.org/0000-0002-6495-9558

Additional information

Funding

The second author is partially supported by NSF grant DMS (Division of Mathematical Sciences) No. 1612891.