“Compress and eliminate” solver for symmetric positive definite sparse matrices

Daria A. Sushnikova, Ivan V. Oseledets

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm applies hierarchically block Gaussian elimination and additionally compresses the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting factorization can be used as an efficient preconditioner and compare the proposed approach with the state-of-art direct and iterative solvers.

    Original languageEnglish
    Pages (from-to)A1742-A1762
    JournalSIAM Journal on Scientific Computing
    Issue number3
    Publication statusPublished - 2018


    • Direct solver
    • Hierarchical matrix
    • Sparse matrix
    • Symmetric positive definite matrix


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