The IDR method for solving large nonsymmetric linear systems

Martin van Gijzen
Department of Applied Mathematical Analysis
Delft University of Technology
Delft, the Netherlands


Krylov subspace methods are used extensively for the iterative solution of linear systems of equations. In the talk we describe IDR(s), a relatively new method for solving nonsymmetric systems. IDR(s) is based on short recursions, which means that only a modest (fixed) number of vectors is needed to carry out the iterative process. It is by now recognized that IDR(s) is among the fastest and most robust short-recurrence methods available. It is always at least as fast as the popular Bi-CGSTAB method, and outperforms the latter for a wide class of problems.

In the talk we will explain the mathematics behind IDR(s), and we will also discuss some recent extensions of the method for computing eigenvalues and for solving linear matrix equations.

We shall illustrate the performance of IDR(s) with academic convection-diffusion-reaction problems and with realistic applications from oceanography and from elastic wave propagation