Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Adaptive preconditioners for nonlinear systems of equations
Journal of Computational and Applied Mathematics
Toward memory-efficient linear solvers
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
SIAM Journal on Scientific Computing
A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
The BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Output error estimation for summation-by-parts finite-difference schemes
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
Accelerated GCRO-DR method for solving sequences of systems of linear equations
Journal of Computational and Applied Mathematics
A block GCROT(m,k) method for linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
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Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become excessive. In practice one has to limit the resources. The most obvious ways to do this are to restart GMRES after some number of iterations and to keep only some number of the most recent vectors in GCR. This may lead to very poor convergence and even stagnation. Therefore, we will describe a method that reveals which subspaces of the Krylov space were important for convergence thus far and exactly how important they are. This information is then used to select which subspace to keep for orthogonalizing future search directions. Numerical results indicate this to be a very effective strategy.