SIAM Journal on Scientific and Statistical Computing
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
An overview of approaches for the stable computation of hybrid BiCG methods
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
A Stabilized QMR Version of Block BiCG
SIAM Journal on Matrix Analysis and Applications
ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Error Estimates and Evaluation of Matrix Functions via the Faber Transform
SIAM Journal on Numerical Analysis
Bi-CGSTAB as an induced dimension reduction method
Applied Numerical 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
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The induced dimension reduction (IDR) method of Sonneveld and van Gijzen [SIAM J. Sci. Comput., 31 (2008), pp. 1035-1062] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML($s$)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petrov-Galerkin methods. The connection with rational Krylov spaces inspired a new version of IDR, called Ritz-IDR, where the poles of the rational function are chosen as certain Ritz values. Experiments are presented illustrating the effectiveness of this new version.