Machine learningKrylov Subspace Iterative
共轭梯度法
共轭梯度（CG）法是一种用于求解大型稀疏对称正定线性方程组 Ax = b 的迭代算法，由 Hestenes 和 Stiefel 于 1952 年开发。它是科学计算中最广泛使用的迭代求解器之一，因为对于 n × n 矩阵，它最多在 n 次迭代内收敛，并且通常需要远少于此次数。
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来源
- Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards, 49(6), 409–436. DOI: 10.6028/jres.049.044 ↗
- Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (2nd ed.). SIAM. DOI: 10.1137/1.9780898718003 ↗
- Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. DOI: 10.1007/978-0-387-40065-5 ↗
如何引用本页
ScholarGate. (2026, June 3). Conjugate Gradient Method for Linear Systems. ScholarGate. https://scholargate.app/zh/numerical-methods/conjugate-gradient-method
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