Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...

accurate calculation of reliability index is very important for the reliability analysis of structures. in some limit state functions with nonlinear characteristic and several local optimum design points, the computational reliability methods may not appropriately determine the failure probability, and iterative reliability approaches may be converged to local optimum design points. in this pap...

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...