Conjugate gradient methods are efficient to minimize differentiable objective functions in large dimension spaces …. Recently, Dai and Yuan introduced a tree-parameter family of nonlinear conjugate gradient methods and show their convergence …

The shortest-residual family of conjugate gradient methods was first proposed by Hestenes and was studied by Pytlak …, and Dai and Yuan. Recently, a no-line-search scheme in conjugate gradient methods was given by Sun and Zhang, and Chen and … Sun. In this paper, we show the global convergence of two shortest-residual conjugate gradient methods (FRSR and PRPSR …

This work deals with the use of the conjugate gradient method in conjunction with an adjoint problem formulation for …, obstacles or cracks, in heat conduction, groundwater flow and tomography problems. Three versions of the conjugate gradient …

understand the behaviour of the conjugate gradient method. The conjugate gradient method converges typically in three phases, an …

and trial functions on uniform meshes discretizes the equation. Three preconditioned conjugate gradient algorithms solve …

Newton method as outer iteration and the preconditioned generalized conjugate gradient methods (CGS and GMRES) as inner …

methods with piecewise linear test and trial functions. The discrete linear system is solved by two different conjugate … gradient algorithms: CGS and GMRES. The preconditioning with Gram matrix approximations consists of replacing the solving of …