# A New Gradient Method with an Optimal Stepsize Property

## Related Articles

- A New Gradient Method with an Optimal Stepsize Property. Dai, Y. H.; Yang, X. Q. // Computational Optimization & Applications;Nov2005, Vol. 32 Issue 3, p73
The gradient method for the symmetric positive definite linear system Ax = b is as follows xk+1 = xk - ak gk where gk = Axk - b is the residual of the system at xk and ak is the stepsize. The stepsize ak = [This symbol can not be represented into ASCI format.] is optimal in the sense that it...

- A parallel preconditioned method for sparse linear systems. LIU Xiu-min; LV Quan-yi; DU Yan-jun // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;Jun2012, Vol. 25 Issue 2, p180
A parallel preconditioned conjugate gradient method is proposed in this manuscript to solve linear systems with a sparse, symmetric and positive coefficient matrix. The preconditioned idea of iteration method is derived. First, given the preconditioner M, the iterative method was constructed to...

- SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS. Li-zhi Cheng // Journal of Computational Mathematics;Mar2001, Vol. 19 Issue 2, p167
Provides information on a study which discussed the properties of eigenvalues for the solutions of symmetric positive definite Toeplitz systems, skew circulant and sine transform based properties. Eigenvalues of various preconditioners; Design of positive sine transform based preconditioners;...

- Quantum time of arrival Goursat problem. Sombillo, Denny Lane B.; Galapon, Eric A. // Journal of Mathematical Physics;Apr2012, Vol. 53 Issue 4, p043702
The construction of quantum time of arrival operator conjugate to the system Hamiltonian leads to a particular linear homogeneous Goursat problem. In this work, we demonstrate how to approximate the solution of the mentioned differential equation both semi-analytically and numerically with the...

- THE GRADIENT METHOD FOR OVERDETERMINED INFINITE LINEAR SYSTEMS. Finta, Béla // Scientific Bulletin of the Petru Maior University of Targu Mures;2012, Vol. 9 Issue 2, p5
It is well known the notion of overdetermined finite linear system and its solution in the sense of the least squares method (see for example [1], [7] or [8]). In [5] we presented the gradient method for overdetermined finite linear systems and in [6] we made the comparative efficiencies of the...

- Preconditioning Newtonâ€“Krylov methods in nonconvex large scale optimization. Fasano, Giovanni; Roma, Massimo // Computational Optimization & Applications;Oct2013, Vol. 56 Issue 2, p253
We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices...

- AN INNER-OUTER REGULARIZING METHOD FOR ILL-POSED PROBLEMS. FAVATI, PAOLA; LOTTI, GRAZIA; MENCHI, ORNELLA; ROMANI, FRANCESCO // Inverse Problems & Imaging;May2014, Vol. 8 Issue 2, p409
Conjugate Gradient is widely used as a regularizing technique for solving linear systems with ill-conditioned coefficient matrix and right-hand side vector perturbed by noise. It enjoys a good convergence rate and computes quickly an iterate, say xkopt, which minimizes the error with respect to...

- Implementations of Affine Scaling Methods: Approximate Solutions of Systems of Linear Equations Using Preconditioned Conjugate Gradient Methods. Mehrotra, Sanjay // ORSA Journal on Computing;Spring92, Vol. 4 Issue 2, p103
The conjugate gradient method has been proposed for solving system of linear equations arising at each iteration of interior point methods. This paper studies several problems associated with developing such implementations. This includes development of a termination criteria, computation of an...

- A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS*[sup 1]). Zhong-zhi Bai; Shao-liang Zhang // Journal of Computational Mathematics;Jul2002, Vol. 20 Issue 4, p437
Presents a class of regularized conjugate gradient methods for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. Discussion on the covergence properties of these methods; Investigation on the new methods...