The Generalized Minimal Residual method (GMRES) seeks optimal approximate solutions of linear system Ax = b from Krylov subspaces by minimizing the residual norm ‖Ax − b‖2 over all x in the subspaces. Its main cost is computing and storing basis vectors of the subspaces. For difficult systems, Krylov subspaces of very high dimensions are necessary for obtaining approximate solutions with desire...

GMRES is an iterative method that provides better solutions when dealing with larg linear systems of equations with unsymmetric coefficient matrix. By shifting the Arnoldi process to begin with Ar0 instead of r0, simpler GMRES implementation, proposed by Walker and Zhou in 1994, is obtained that in this method, an upper triangular problem is solved instead of hessenberg least square problem. Th...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 15 June 2020Accepted: 22 February 2021Published online: 14 2021KeywordsKaczmarz method, randomized algorithm, linear system, overdetermined underdetermined least squares problem, iterative inner-outer iteration, preconditioner, GMRES, flexible GMRESAMS Subject Headings65F...

this study proposes a modified version of cultural algorithms (cas) which benefits from rule-based system for influence function. this rule-based system selects and applies the suitable knowledge source according to the distribution of the solutions. this is important to use appropriate influence function to apply to a specific individual, regarding to its role in the search process. this rule ...

the cuckoo search algorithm is a recently developedmeta-heuristic optimization algorithm, which is suitable forsolving optimization problems. to enhance the accuracy andconvergence rate of this algorithm, an improved cuckoo searchalgorithm is proposed in this paper. normally, the parametersof the cuckoo search are kept constant. this may lead todecreasing the efficiency of the algorithm. to cop...

in this paper, a new continuous ant colony optimization (caco) algorithm is proposed for optimal reservoir operation. the paper presents a new method of determining and setting a complete set of control parameters for any given problem, saving the user from a tedious trial and error based approach to determine them. the paper also proposes an elitist strategy for caco algorithm where best solut...

We introduce an iterative method named Gpmr (general partitioned minimum residual) for solving block unsymmetric linear systems. is based on a new process that simultaneously reduces two rectangular matrices to upper Hessenberg form and closely related the block-Arnoldi process. tantamount Block-Gmres with right-hand sides in which approximate solutions are summed at each iteration, but its sto...

We investigate the convergence of GMRES for an n by n Jordan block J . For each k that divides n we derive the exact form of the kth ideal GMRES polynomial and prove the equality max ‖v‖=1 min p∈πk ‖p(J)v‖ = min p∈πk max ‖v‖=1 ‖p(J)v‖, where πk denotes the set of polynomials of degree at most k and with value one at the origin, and ‖ · ‖ denotes the Euclidean norm. In other words, we show that ...

We experimentally examine the performance of preconditioners based on entries of the symmetric positive definite part and small subspace solvers for linear system of equations obtained from the high-order compact discretization of convection-diffusion equations. Numerical results are described to illustrate that the preconditioned GMRES algorithm converges in a reasonable number of iterations.

Control systems have always been a vital part of the novel technological advancements of human being in any industry, especially transportation. With the introduction of the idea of autonomous driving, classical control systems are not effective anymore and the need for intelligent control systems is inevitable. Advanced Driver Assistance Systems (ADASs), which are systems proposed to help driv...