مقایسهٔ روش‌ها

	روش گرادیان مزدوج	GMRES
حوزه	روش‌های عددی	روش‌های عددی
خانواده	Machine learning	Machine learning
سال پیدایش	1952	1986
پدیدآور	Magnus Hestenes and Eduard Stiefel	Youcef Saad and Martin H. Schultz
نوع	Iterative linear solver	Iterative linear solver for non-symmetric systems
منبع بنیادین	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.
نام‌های دیگر	CG method, Krylov subspace method	GMRES(m), restarted GMRES, Krylov-GMRES
مرتبط	1	1
خلاصه	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.