Machine learningKrylov Subspace Iterative
GMRES
GMRES（广义最小残差法）是由 Saad 和 Schultz 于 1986 年开发的一种求解大型稀疏非对称线性方程组 Ax = b 的迭代方法。它使用阿诺尔迪方法构建正交的 Krylov 基，并在每次迭代中求解最小二乘问题以最小化残差。
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来源
- Saad, Y., & Schultz, M. H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7(3), 856–869. DOI: 10.1137/0907058 ↗
- Walker, H. F. (1988). Implementation of the GMRES method using Householder reflections. SIAM Journal on Scientific and Statistical Computing, 9(1), 152–163. DOI: 10.1137/0909010 ↗
- Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (2nd ed.). SIAM. DOI: 10.1137/1.9780898718003 ↗
如何引用本页
ScholarGate. (2026, June 3). Generalized Minimal Residual Method. ScholarGate. https://scholargate.app/zh/numerical-methods/gmres
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