手法を比較

	共役勾配法	GMRES
分野	数値解析	数値解析
系統	Machine learning	Machine learning
提唱年	1952	1986
提唱者	Magnus Hestenes and Eduard Stiefel	Youcef Saad and Martin H. Schultz
種類	Iterative linear solver	Iterative linear solver for non-symmetric systems
原典	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.	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.
別名	CG method, Krylov subspace method	GMRES(m), restarted GMRES, Krylov-GMRES
関連	1	1
概要	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.