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<p>This paper proposes an effective Schur complement based parallel preconditioner for solving general large sparse linear systems. The basic idea of this new preconditioning procedure is to transform a given original problem into several smaller systems that can be solved in parallel. The preconditioner is based on the domain multicoloring ordering and combines the Schur complement technique with low-rank corrections, and is different from the available existing Schur complement based preconditioners. Each smaller system corresponds to a color and a “local" solution. Numerical examples illustrate that the proposed preconditioner accelerates Krylov subspace iterative methods for large sparse linear systems considerably.</p>

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A Schur complement based multicoloring low-rank correction preconditioner for linear systems

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • QingQing Zheng

摘要

This paper proposes an effective Schur complement based parallel preconditioner for solving general large sparse linear systems. The basic idea of this new preconditioning procedure is to transform a given original problem into several smaller systems that can be solved in parallel. The preconditioner is based on the domain multicoloring ordering and combines the Schur complement technique with low-rank corrections, and is different from the available existing Schur complement based preconditioners. Each smaller system corresponds to a color and a “local" solution. Numerical examples illustrate that the proposed preconditioner accelerates Krylov subspace iterative methods for large sparse linear systems considerably.