求解复对称线性系统的极小化残差广义位移分裂迭代法
Minimal Residual Generalized Shift-Splitting Iterative Method for Solving Complex Symmetric Linear Systems
摘要: 在科学计算和工程应用中，许多问题最终均可归结为求解大型稀疏复对称线性系统。针对此类系统的求解，本文将极小化残差技术应用至广义位移分裂(GSS)迭代过程，构造了极小化残差GSS (MRGSS)迭代法，推导了该方法的代数降维求解策略，并给出了严格的收敛性分析。最后，通过数值实验验证了所提方法的高效性。
Abstract: In scientific computing and engineering applications, many problems can ultimately be reduced to solving large sparse complex symmetric linear systems. For the solution of such systems, this paper applies the minimization residual technique to the generalized shift-splitting (GSS) iterative process, constructs the minimization residual GSS (MRGSS) iterative method, derives the algebraic dimension reduction solution strategy of this method, and provides a strict convergence analysis. Finally, the efficiency of the proposed method is verified through numerical experiments.
文章引用：梁媛媛. 求解复对称线性系统的极小化残差广义位移分裂迭代法[J]. 应用数学进展, 2026, 15(5): 367-377. https://doi.org/10.12677/aam.2026.155236

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