Interpreting IDR(s) as a deflation method

In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the deflated system in each IDR(s) cycle to all...

Exploiting the flexibility of IDR(s) for grid computing

The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s)...

Fast iterative solution of large sparse linear systems on geographically separated clusters

Parallel scientific computing on loosely coupled networks of computers

Solving large sparse linear systems efficiently on grid computers using an asynchronous iterative method as a preconditioner

Implementing the conjugate gradient method on a grid computer

Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm...