求解一类复对称线性系统的优化的结构预处理子

Optimized Structured Preconditioner for a Class of Complex Symmetric Linear Systems

  • 摘要: 针对一类复对称线性系统,提出一个优化的结构预处理子.当用于加速特定的Krylov子空间方法时,该预处理子可导出不依赖网格尺寸的稳定数值表现.理论分析了该预处理子的计算复杂性,并表明相应预处理矩阵的特征值是正实的且分布在\left\frac12+\frac\varepsilon2 \sqrt1+\varepsilon^2, 1\right.数值结果验证了理论推导的正确性,并表明了该预处理子的有效性和稳定性.

     

    Abstract: An optimized structured (OS) preconditioner for a class of complex symmetric linear systems is proposed. The OS-preconditioner results in a fast Krylov subspace solver, which is robust with respect to the mesh-size. The computational complexity of OS-preconditioner is analyzed and it is shown that all eigenvalues of the corresponding preconditioned matrix are positive real and distributed on \left\frac12+\frac\varepsilon2 \sqrt1+\varepsilon^2, 1\right. Numerical experiments confirming the theoretical derivations are presented to verify the effectiveness and stability of the OS-preconditioner.

     

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