方法对比
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| 共轭梯度法× | GMRES× | |
|---|---|---|
| 领域 | 数值方法 | 数值方法 |
| 方法族 | Machine learning | Machine learning |
| 起源年份≠ | 1952 | 1986 |
| 提出者≠ | Magnus Hestenes and Eduard Stiefel | Youcef Saad and Martin H. Schultz |
| 类型≠ | Iterative linear solver | Iterative linear solver for non-symmetric systems |
| 开创性文献≠ | 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 ↗ | 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 ↗ |
| 别名≠ | CG method, Krylov subspace method | GMRES(m), restarted GMRES, Krylov-GMRES |
| 相关 | 1 | 1 |
| 摘要≠ | The Conjugate Gradient (CG) Method is an iterative algorithm for solving large sparse symmetric positive-definite linear systems Ax = b, developed by Hestenes and Stiefel in 1952. It is one of the most widely used iterative solvers in scientific computing because it converges in at most n iterations for an n × n matrix and typically requires far fewer. | GMRES (Generalized Minimal Residual) is an iterative method for solving large sparse non-symmetric or nonsymmetric linear systems Ax = b, developed by Saad and Schultz in 1986. It builds an orthonormal Krylov basis using Arnoldi's method and solves a least-squares problem to minimize residual at each iteration. |
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