On projected Newton-Krylov solvers for instationary laminar reacting gas flows
Journal of Computational Physics
GBi-CGSTAB(s,L): IDR(s) with higher-order stabilization polynomials
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A comparative study of iterative solutions to linear systems arising in quantum mechanics
Journal of Computational Physics
The Iterative Solver RISOLV with Application to the Exterior Helmholtz Problem
SIAM Journal on Scientific Computing
Interpreting IDR as a Petrov-Galerkin Method
SIAM Journal on Scientific Computing
Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
SIAM Journal on Scientific Computing
A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method
Journal of Computational and Applied Mathematics
Algorithm 913: An elegant IDR(s) variant that efficiently exploits biorthogonality properties
ACM Transactions on Mathematical Software (TOMS)
A variant of the IDR(s) method with the quasi-minimal residual strategy
Journal of Computational and Applied Mathematics
Experience in developing an open source scalable software infrastructure in japan
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
Solution of generalized shifted linear systems with complex symmetric matrices
Journal of Computational Physics
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
A variant of IDRstab with reliable update strategies for solving sparse linear systems
Journal of Computational and Applied Mathematics
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
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We present IDR($s$), a new family of efficient, short-recurrence methods for large nonsymmetric systems of linear equations. The new methods are based on the induced dimension reduction (IDR) method proposed by Sonneveld in 1980. IDR($s$) generates residuals that are forced to be in a sequence of nested subspaces. Although IDR($s$) behaves like an iterative method, in exact arithmetic it computes the true solution using at most $N + N/s$ matrix-vector products, with $N$ the problem size and $s$ the codimension of a fixed subspace. We describe the algorithm and the underlying theory and present numerical experiments to illustrate the theoretical properties of the method and its performance for systems arising from different applications. Our experiments show that IDR($s$) is competitive with or superior to most Bi-CG-based methods and outperforms Bi-CGSTAB when $s 1$.