השוואת שיטות

	שיטת הגרדיאנטים הצמודים	GMRES
תחום	שיטות נומריות	שיטות נומריות
משפחה	Machine learning	Machine learning
שנת המקור	1952	1986
הוגה השיטה	Magnus Hestenes and Eduard Stiefel	Youcef Saad and Martin H. Schultz
סוג	Iterative linear solver	Iterative linear solver for non-symmetric systems
מקור מכונן	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.
כינויים	CG method, Krylov subspace method	GMRES(m), restarted GMRES, Krylov-GMRES
קשורות	1	1
תקציר	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.