The Induced Dimension Reduction method and extensions for solving large systems of linear equations

Gerard L. G. Sleijpen
Department of Mathematics
Utrecht University
Utrecht, The Netherlands


The Induced Dimension Reduction method (IDR(s)) (2008) and BiCGstab(l) (1993) are two of the most efficient short recurrence iterative methods for solving large sparse nonsymmetric linear systems. Which of the two is best depends on the specific problem class. IDRstab combines the strengths of both. We will discuss extensions to include
- QMR smoothing (as for BiCGstab(l) convergence of IDR(s) can be irregular),
- a method for solving shifted systems with many shifts (multi-shift),
- flexible preconditioning, and
- deflation.