A preconditioned inexact Jacobi–Davidson method for the computation of the eigenpairs of large and sparse symmetric matrices is proposed. In each inner iteration step of Jacobi–Davidson method, two preconditioners based on a regularization method and shift-splitting of the saddle point matrix are given. Then the properties of the preconditioned matrix are investigated. Numerical results illustrate that the new proposed algorithms are more efficient than Jacobi–Davidson method.

中文翻译：

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大对称特征值问题的预处理不精确Jacobi-Davidson方法

提出了一种预处理的不精确的Jacobi-Davidson方法，用于计算大型稀疏对称矩阵的本征对。在Jacobi–Davidson方法的每个内部迭代步骤中，给出了两个基于正则化方法和鞍点矩阵移位分裂的预处理器。然后研究预处理矩阵的性质。数值结果表明，新提出的算法比Jacobi–Davidson方法更有效。