- Referenced in 200 articles
- that arise. Two others use iterative (preconditioned Krylov) methods instead of direct methods for these...
- Referenced in 140 articles
- terminate the iterations earlier. A preconditioned truncated Newton method is described that defines a search...
- Referenced in 50 articles
- direct method or a preconditioned iterative method...
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- accelerated algebraic multigrid and preconditioned iterative methods. The solution of large sparse linear systems arises ... distributed algebraic multigrid (AMG) and preconditioned iterative methods. The AmgX library implements both classical ... aggregation-based AMG methods with different selector and interpolation strategies, along with a variety ... standard and flexible preconditioned Krylov subspace iterative methods, which can be combined with...
- Referenced in 253 articles
- algorithms for discretization by mixed finite element methods and a posteriori error estimation ... experimenting with state-of-the-art preconditioned iterative solvers for the discrete linear equation systems...
- Referenced in 40 articles
- primal-infeasible dual-feasible network interior point method The authors introduce the truncated primal-infeasible ... minimum-cost network flow problem. In each iteration, the linear system that determines the search ... implementation, a preconditioned conjugate gradient method is used as the iterative solver. The details...
- Referenced in 146 articles
- advocate the standard preconditioned conjugate gradient method for finding an eigenvector as an element ... known. We recommend that every new preconditioned eigensolver be compared with this “ideal” algorithm ... every iteration, and memory requirements. We provide such comparison for our LOBPCG method. Numerical results...
- Referenced in 65 articles
- paper describes new recursive multilevel method for preconditioning of general sparse linear systems. This strategy ... authors’ codes BILUM and BILUTM. All these methods are based on a block incomplete ... reordering and inner-level iterations. Assumptions, under which the new preconditioning is exact, are given ... with the proof that eigenvalues of the preconditioned matrix are close to 1. par Extensive...
- Referenced in 43 articles
- methods (RTRMC 2) and Riemannian conjugate gradient methods (RCGMC) to solve it. A preconditioner ... detail preconditioned versions of Riemannian optimization algorithms. The cost of each iteration is linear ... number of known entries. The proposed methods are competitive with state-of-the-art algorithms ... further note that second-order and preconditioned methods are well suited to solve badly conditioned...
- Referenced in 113 articles
- generate a Cauchy step, a preconditioned conjugate gradient method with an incomplete Cholesky factorization ... generating a small number of minor iterates, even for problems with a large number...
- Referenced in 99 articles
- introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems ... method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods ... great flexibility in addressing problem specificity through preconditioning and other means and allows easy adaptation...
- Referenced in 24 articles
- iterative solvers instead of the routinely used direct factorization techniques. The preconditioned conjugate gradient method...
- Referenced in 20 articles
- objective function be convex. The methods are iterative at two levels, one level relating ... preconditioned conjugate gradient method is used for this inner iteration, with the preconditioner chosen especially...
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- large number of iterative methods, preconditioners, and other variants for iterative solvers and provides ... like automatic adaptation to more robust preconditioned iterative methods. Two distributed-memory parallel processors, namely...
- Referenced in 4 articles
- more robust than other available preconditioned iterative methods, and more scalable than parallel sparse direct...
- Referenced in 9 articles
- linear systems, and has 13 iterative methods and 7 preconditioning methods. The purpose ... most difficult and error-prone part of iterative solvers. The price to be paid...
- Referenced in 27 articles
- Block Preconditioned Conjugate Gradient Method (LOBPCG). Its main features are: a matrix-free iterative method...
- Referenced in 11 articles
- usual overhead by preconditioning the implicit method with an iterative technique. This results...
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- distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing...
- Referenced in 35 articles
- called “NSPCG” since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed ... equations by a variety of different iterative methods. One of the main purposes...