# The IDR method for solving large nonsymmetric linear systems

**Martin van Gijzen
**

Department of Applied Mathematical Analysis

Delft University of Technology

Delft, the Netherlands

### Abstract:

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